Amorphous and crystalline forms of smilagenin and its hydrates

ABSTRACT

The invention provides smilagenin in novel amorphous, crystalline, hydrated and solvated forms, and the use thereof in manufacturing pharmaceutical or edible grade smilagenin and its derivatives.

FIELD OF THE INVENTION

The present invention relates to novel amorphous and crystalline forms of smilagenin and its hydrates.

BACKGROUND TO THE INVENTION

It is well established that some organic compounds can crystallise in a number of different polymorphic forms or crystal habits, which may comprise the compound as such, solvates of the compound, hydrates of the compound, or combinations thereof. Alternatively, the compound, solvate or hydrate may precipitate as an amorphous solid.

The stability and bioavailability of the drug product may vary according to the polymorphic form present. The choice of crystal form is thus a critical aspect of drug development (Brittain, Pharm. Tech. pp. 50-52, 1994; Yu et al., Pharm. Sci. Technol. Today, 1, pp. 118 to 127, 1998; Byrn et al., Chem. Mater. 6, pp. 1148 to 1158, 1994; Byrn et al., Pharm. Res., 12, pp. 945 to 954, 1995; Henk et al., Pharm. Ind. 59, pp. 165 to 169, 1997).

Smilagenin is an A/B-cis steroidal sapogenin having the formula:

Smilagenin and its derivatives have been identified as valuable therapeutic agents in human and veterinary medicine and in non-therapeutic human and non-human animal treatments. See, for example, U.S. Pat. No. 3,890,438 (use of smilagenin and certain 4-substituted phenoxyisobutyric acid compounds against high blood cholesterol levels); U.S. Pat. No. 4,680,289 (use of smilagenin against obesity and diabetes obesity syndromes); U.S. Pat. No. 6,258,386 (use of smilagenin against cognitive dysfunction and allied conditions); WO-A-01/23406, WO-A-01/23407, WO-A-01/23408, and WO-A-01/49703 (use of smilagenin derivatives against cognitive dysfunction and allied conditions); and WO-A-02/079221 and WO-A-03/082893 (use of smilagenin and derivatives thereof against non-cognitive neurodegeneration, non-cognitive neuromuscular degeneration, motor-sensory neurodegeneration and loss of receptor function in the absence of cognitive, neural or neuromuscular impairment).

In a key article (Marker et al., J. Am. Chem. Soc. 65, pp. 1199 to 1209, 1943, at p. 1207), it was reported that smilagenin acetate shows polymorphic forms melting at 110, 130 and 152° C. The melting point of smilagenin from a number of sources was always in the range 183-185° C. However, the recrystallisation solvent was not stated and the article made no mention of polymorphic forms of smilagenin.

In J. Am. Chem. Soc. pp. 2525 to 2532, 1940, Marker et al. reported a melting point of 183-185° C. for smilagenin crystallised from alcohol.

In J. Am. Chem. Soc. 64, pp. 818 to 822, 1942, Marker et al. reported a melting point of 178-180° C. for smilagenin crystallised from acetone.

Askew et al. reported that fractional crystallisation of smilagenin from acetone gave long silky needles with a melting point of 183-184° C. It was further reported that smilagenin appeared to form a hydrate when crystallised from methanol (Askew et al., J. Chem. Soc. pp. 1399 to 1403, 1936). However, no evidence was provided to support this observation, and the reader was merely referred back to an earlier paper on a related compound (Power et al., J. Chem. Soc., 105, pp. 201 to 219, 1914).

Scheer et al. crystallised smilagenin from aqueous ethanol and observed a melting point of 187-188° C., but made no mention of the formation of a hydrate (Scheer et al., J. Am. Chem. Soc., 77, pp. 641 to 646, 1955).

In J. Am. Chem. Soc., 77, pp. 3086 to 3089, 1955, Wall et al. commented that the best samples of smilagenin from natural sources had a melting point of 188-189° C., whereas acetone or aqueous acetone failed to bring the melting point above 182-185° C. on samples generated by isomerization of sarsasapogenin. Again, no mention was made of hydrate formation. The infra-red (IR) spectra of the synthetic and natural materials were identical. However, the X-ray powder diffraction (XRPD) patterns were not. These differences were not attributed to polymorphism, and the XRPD patterns were not presented. The authors concluded that there was a pronounced effect of traces of sarsasapogenin on certain properties of smilagenin that depend on crystal structure.

Wall et al., (J. Biol. Chem., 198, pp. 533 to 543, 1952) reported the melting point of smilagenin to be 184° C. However, the recrystallisation solvent was not stated. The paper reported that the use of a Kofler microscopic melting point apparatus having polarizing disks allowed for the crystal form or habit to be observed. No mention was made of polymorphisin but the impact of impurities upon the melting point was noted. In J. Am. Chem. Soc., 77, pp. 1230 to 1237, 1954, Wall et al. reported the melting point of smilagenin to be 183° C.

Callow et al. (J. Am. Chem. Soc. 77, p. 1672, 1955) described the recrystallisation of smilagenin from acetone to yield crystals having melting point 157-160° C.

Parsons et al. (Henry Ford Hosp. Med. Bull., 12, pp. 87 to 120, 1964) described a specific crystalline form of smilagenin by XRPD. From the data presented it cannot be concluded that this form corresponds to any of the forms described herein.

In U.S. Pat. No. 3,169,959 (1965), a melting point of 178-180° C. was reported for smilagenin crystallised from heptane.

In Phytochemistry, 8, pp. 1523 to 1531, 1969, Blunden et al. reported a melting point of 181-182° C. for smilagenin crystallised from acetone.

In J. Nat. Prod., 44, pp. 441 to 447, 1981, Blunden et al. reported a melting point of 186° C. for smilagenin crystallised from acetone.

The use of crystalline intermediate complexes to assist the extraction of relatively pure smilagenin and other sapogenins from their plant sources has been proposed. Thus, for example, U.S. Pat. No. 5,017,562 described a crystalline saponin-containing complex, derived from the saponin-containing plants Agave, Yucca, Dioscorea, Quillaja, Medicago and Cyamopsis, which is substantially free of fats and non-saponin carbohydrates and which, on hydrolysis, can yield smilagenin and other sapogenins.

The prior art publications acknowledged above are incorporated herein by reference.

Depending on the administration route desired in the therapy, it may be desirable to improve or at least control the stability and water solubility of the smilagenin, to obtain a desired bioavailability profile. Furthermore, it can assist the manufacturing or purification process if the stability and water solubility of the smilagenin can be controlled.

In principle, the water solubility of polymorphic forms of an organic compound is not necessarily the same for all forms. Therefore, the use of specific crystalline forms or habits can offer useful control of the water solubility. In the case of sparingly water-soluble compounds such as smilagenin, even a slight adjustment to the water-solubility by means of an adjustment to the polymorphic form can offer useful processing or biological advantages.

We have examined commercially available smilagenin and have found that it occurs in a specific crystalline form, which we have characterised as form II.

FIG. 1 of the accompanying drawings shows an XRPD pattern obtained at λ=1.5406 Angstroms from a sample of commercially available smilagenin obtained from Research Plus, Inc. This is an example of form II crystalline smilagenin. The intensities of the XRPD pattern for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form II”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation. For present purposes, the approximately 20 strongest peaks may generally be considered characteristic of the crystalline form, subject however to standard practice in crystallography.

The present invention is based on our surprising finding that at least three further crystalline forms of smilagenin exist, two of which appear typically to be anhydrous and have been characterised as form I and form III. We have further found that form III can exist in at least one variant form in which the crystal structure is modified (“form IIIA”) and/or the hydration level is modified (smilagenin hemihydrate or smilagenin dihydrate). Furthermore, we have surprisingly found that smilagenin can form a crystalline monohydrate. We have characterised the typical crystalline form of this monohydrate as form V. Furthermore, we have surprisingly found that smilagenin can form a crystalline channel hydrate having variable smilagenin:water stoichiometry. We have characterised the typical crystalline form of this channel hydrate as form VI. It has also been found that smilagenin can be obtained in a non-crystalline form (the “amorphous form”). The prior art does not describe any amorphous form of smilagenin.

Furthermore, we have identified a crystalline solvate of smilagenin formed with iso-propyl alcohol. We have characterised the typical crystalline form of this iso-propyl alcohol solvate as form VII.

Surprisingly, we have found that form II of smilagenin can be converted to the monohydrate by a solvent mediated transformation in hexane or heptane. Further, we have found that the monohydrate may be obtained by other processes, including solvent mediated transformations in aqueous acetone, aqueous tetrahydrofuran and aqueous ethanol. The water content was determined by Karl Fischer analysis was found to be in the range about 3 to 6% w/w. Analysis by thermogravimetric analysis (TGA) confirms a water weight in the region of 4%.

Furthermore, we have found methods of controlling the transitions between not only the novel amorphous and crystalline forms but between them and the known form II, by controlling the organic solvent used for recrystallisation.

Surprisingly, and advantageously, we have found that precipitation or crystallisation of smilagenin from certain organic solvents does not result in organic solvates of smilagenin. However, the iso-propyl alcohol solvate (believed to be a hemi-solvate) can be obtained under certain circumstances, and is a newly recognised material.

These novel forms of smilagenin and associated methods therefore offer enhanced control of the preparation of pharmaceutical or edible grade smilagenin, and the possibility of preparing pharmaceutical or edible grade smilagenin with improved delivery and bioavailability characteristics.

BRIEF DESCRIPTION OF THE INVENTION

According to a first aspect of the present invention, there is provided smilagenin in any one or more of crystalline forms I, III, IIIA, V, VI and VII as defined herein.

According to an example of this first aspect of the present invention, there is provided smilagenin in any one or more of crystalline forms I, III, IIIA and V as defined herein.

According to a second aspect of the present invention, there is provided smilagenin hemihydrate, optionally in crystalline form.

According to a third aspect of the present invention, there is provided smilagenin monohydrate, optionally in crystalline form.

According to a fourth aspect of the present invention, there is provided smilagenin dihydrate, optionally in crystalline form.

According to a fifth aspect of the present invention, there is provided smilagenin channel hydrate, optionally in crystalline form.

According to a sixth aspect of the present invention, there is provided amorphous smilagenin.

According to a seventh aspect of the present invention, there is provided smilagenin iso-propyl alcohol solvate, optionally in crystalline form. This material may be prepared by precipitation from a solution of relatively impure smilagenin in iso-propyl alcohol that has been reduced in volume by azeotropic distillation.

According to an eighth aspect of the present invention, there is provided crystalline pharmaceutical or edible grade anhydrous unsolvated smilagenin, when obtained by crystallisation from a solution of substantially pure smilagenin iso-propyl alcohol (IPA) solvate in an anhydrous IPA-compatible organic solvent which does not form a solvate with smilagenin, such as acetone. The smilagenin may be in crystalline form I or III as defined herein.

The crystalline or amorphous material of the present invention may be present substantially free of other forms of smilagenin and/or substantially free of other steroidal sapogenins and/or steroidal saponins.

The crystalline or amorphous material of the present invention may preferably be present in at least about 50% by weight pure form, for example at least about 70% by weight pure form, for example at least about 80% by weight pure form, for example at least about 85% by weight pure form, for example at least about 90% by weight pure form, for example at least about 95% by weight pure form, for example at least about 97% by weight pure form, for example at least about 98% by weight pure form.

Any of the materials according to the present invention may if desired be present in admixture with one or more other materials according to the present invention, another form of smilagenin, any other biologically active material, any biologically inactive material, or any combination thereof. The said other form of smilagenin, when present, may be crystalline form II.

The novel forms of smilagenin provided by the present invention possess a number of advantages over the known form, particularly in terms of their stability and handling characteristics. These advantages are applicable to one or more of the manufacturing, purification, formulation and storage phases of the marketed smilagenin compositions and/or to the delivery of the smilagenin from the composition to the human or non-human animal patient for achieving the desired pharmacological effect.

The present invention also provides methods for preparing the materials of the present invention, preferably by precipitation of smilagenin from a solution of smilagenin in an appropriate organic solvent or solvent mixture or by other crystallisation of smilagenin in an appropriate organic solvent or solvent mixture, optionally in the presence of water, as well as medicaments, foodstuffs and beverages containing the said materials, methods of preparing the medicaments, foodstuffs and beverages, uses of the said materials in the preparation of the medicaments, foodstuffs and beverages, and uses of the medicaments, foodstuffs and beverages in human and veterinary medicine and in non-therapeutic human and non-human animal treatments.

The present invention further provides a process for obtaining pharmaceutical or edible grade smilagenin or a derivative thereof, wherein at least one step of the process includes preparing smilagenin in one or more of the forms according to the present invention. The smilagenin may be prepared in any suitable level of hydration and in any suitable physical form, for example as an isolated dry solid or in a liquid medium such as a crystal slurry.

The resultant pharmaceutical or edible grade smilagenin or derivative thereof may be subsequently formulated into a suitable medicament, foodstuff or beverage form.

The present invention further provides methods of adjusting the crystalline form of smilagenin between the forms I, II, III, IIIA, V, VI and VII (for example between the forms I, II, III, IIIA and V), methods of adjusting the form of smilagenin between its amorphous and crystalline forms, methods of adjusting the hydration level of smilagenin, methods of forming the iso-propyl alcohol solvate of smilagenin and methods of adjusting the form of smilagenin between two or more of the hydrated, solvated and unhydrated and unsolvated forms.

The terms “crystallise”, “recrystallise” and the like, used herein, refer to all methods suitable for forming a desired crystal form or habit or mixture or other combination thereof, and are not limiting. For example, crystal slurrying, crystal precipitation, and other solvent mediated crystal transformation, with or without seeding and/or nucleation, are all encompassed by the terms “crystallise”, “recrystallise” and the like as used herein.

The materials according to the present invention may therefore conveniently be present in substantially pure isolated form. The materials may suitably be prepared on a kilogram scale.

DETAILED DESCRIPTION OF THE INVENTION Crystalline Form I

The term “crystalline form I” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 2 of the accompanying drawings (λ=1.5406 Angstroms).

The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.

The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form I”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation.

The form I material can be prepared by recrystallisation of commercially available smilagenin from acetone. Alternatively, the form I material can be prepared by a solvent mediated transformation of form II or form III material in acetone, or more preferably in acetonitrile.

Karl Fischer analysis, differential scanning calorimetry and thermogravimetric analysis confirmed that the crystal form I that we have obtained is neither hydrated nor solvated.

Crystalline Form II

The term “crystalline form II” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 1 of the accompanying drawings (λ=1.5406 Angstroms).

The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.

The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form II”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation.

The form II material was commercially available smilagenin obtained from Research Plus, Inc.

Differential scanning calorimetry (DSC), TGA, residual solvent and Karl Fischer analysis confirmed that the material was neither hydrated nor solvated.

Crystalline Form III

The term “crystalline form III” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 3 of the accompanying drawings (λ=1.5406 Angstroms).

The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.

The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form III”. These data are the intensities at regularly spaced 2-theta values, and are to be used in conjunction with the Figure of the drawings. From these data, the d-spacings may readily be calculated using the Bragg equation.

The form III material may be prepared by solvent mediated transformation of commercially available smilagenin using methyl t-butyl ether, acetone, methyl iso-butyl ketone, ethyl acetate, iso-propyl acetate and toluene.

Solvent mediated transformations of commercially available smilagenin using butanone or from 50% aqueous ethanol yielded a mixture of crystal forms III and V.

These data show that crystal form II can be converted into form III by solvent mediated transformations using a range of solvents.

Karl Fischer analysis, differential scanning calorimetry and thermogravimetric analysis confirmed that the crystal form III that we have obtained is neither hydrated nor solvated.

Crystalline Form IIIA

The term “crystalline form IIIA” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 4 of the accompanying drawings (λ=1.5406 Angstroms).

The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.

The d-spacings may readily be calculated from the information in FIG. 4, using the Bragg equation.

The form IIIA material may be prepared by a solvent mediated transformation of commercially available smilagenin using dimethylformamide.

Crystalline Form V

The term “crystalline form V” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIG. 5 of the accompanying drawings (λ=1.5406 Angstroms).

The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 5 to 50 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.

The intensities of the XRPD peaks for this crystalline form in the 2-theta range 5 to 50 degrees are shown in Table A below, in the column headed “Form V”. From this data, the d-spacings may readily be calculated using the Bragg equation.

The form V material may be prepared in relatively pure form by recrystallisation of commercially available smilagenin from ethanol, tetrahydrofuran, hexane or aqueous acetone. The acetone/water proportions in the aqueous acetone may vary widely, for example from about 0.5:1 (by volume) to about 25:1 (by volume), for example from about 1:1 (by volume) to about 20:1 (by volume), for example from about 2:1 (by volume) to about 19:1 (by volume),

A solvent mediated transformation of commercially available smilagenin in butanone or in 50% aqueous ethanol yielded a mixture of crystal forms III and V.

A solvent mediated transformation of commercially available smilagenin in dichloromethane yielded a mixture of crystal forms II and V.

Solvent mediated transformations in aqueous acetone, aqueous tetrahydrofuran or aqueous ethanol all yield crystal form V (monohydrate). In each case the proportions of water to solvent in the medium can vary widely. The purity of the resultant crystalline material appears to be higher when aqueous acetone is used, in comparison with the alternative media.

Karl Fischer analysis, DSC (FIG. 6) and TGA (FIG. 7) confirmed that the crystal form V that we have obtained is a monohydrate of smilagenin.

Crystalline Form VI

The term “crystalline form VI” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIGS. 8 and 15 of the accompanying drawings (λ=1.5406 Angstroms).

The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 2 to 28 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.

The intensities of the XRPD peaks for this crystalline form in the 2-theta range 2 to 28 degrees can be obtained from FIGS. 8 and 15. The 29 and d-spacings for the significant peaks, and the intensities of the significant peaks relative to the strongest peak, are given in Table B.

The form VI material may be prepared in relatively pure form by recrystallisation of commercially available smilagenin from methanol.

DSC (FIG. 9), TGA (FIG. 10) and vapour sorption (FIG. 11) analysis suggest that the crystal form VI that we have obtained is a channel hydrate of smilagenin exhibiting variable smilagenin:water stoichiometry and the potential to form channel solvates with solvents having appropriately sized molecules. As is well known, a channel hydrate is a hydrate in which the crystal lattice of the molecule forms a channel or cage enclosing a void which can wholly or partially accommodate water (or solvent) molecules. The stoichiometric (molar) ratio of smilagenin:water at any particular time will depend on such factors as the humidity of the surrounding atmosphere, as the water molecules are generally free to enter or leave the void.

Crystalline Form VII

The term “crystalline form VII” used herein means that crystalline form of smilagenin which has an XRPD pattern substantially as shown in FIGS. 12 and 16 of the accompanying drawings (λ=1.5406 Angstroms).

The expression “an XRPD pattern substantially as shown” as used herein refers particularly to any XRPD pattern having 2-theta or d-spacing peaks corresponding to the diagnostic peaks of the Figure. For present purposes, the approximately 20 strongest peaks in the 2-theta range 2 to 28 degrees may generally be considered characteristic or diagnostic of the crystalline form, subject however to standard practice in crystallography.

The intensities of the XRPD peaks for this crystalline form in the 2-theta range 2 to 28 degrees can be obtained from FIGS. 12 and 16. The 20 and d-spacings for the significant peaks, and the intensities of the significant peaks relative to the strongest peak, are given in Table C.

The form VII material may be prepared in relatively pure form by crystallisation of smilagenin from iso-propyl alcohol (IPA). The material may subsequently be aged if desired (e.g. at ambient temperature and e.g. for a period of at least about 24 hours, for example at least about 48 hours). If desired, the form VII material may be subsequently recrystallised from acetone to afford anhydrous unsolvated smilagenin in substantially pure form. DSC (FIG. 13) and TGA (FIG. 14) indicate that the crystal form VII that we have obtained is a hemi-IPA solvate of smilagenin.

The form VII material is potentially important as an intermediate in the purification of smilagenin to produce pharmaceutical or edible grade smilagenin. Without wishing to be bound by theory, it is believed that a solution of relatively impure smilagenin in iso-propyl alcohol is especially convenient for being azeotropically distilled in order to efficiently remove water from the solution. The IPA solvate of smilagenin which is precipitated from the reduced solution after the said distillation can conveniently be recrystallised as pharmaceutical or edible grade anhydrous unsolvated smilagenin using an anhydrous IPA-compatible organic solvent such as acetone, which does not form a solvate with smilagenin.

Therefore, in one particular embodiment, the form VII material may be in substantially pure isolated, preferably dry, form and prepared by precipitation from a solution of relatively impure smilagenin in iso-propanol, which solution has preferably previously undergone distillation to reduce its volume and remove water or other impurities. Most preferably, the process by which the form VII material is made is conducted on an industrial scale (obtaining at least kilogram quantities of the form VII material). Preferably, anhydrous unsolvated smilagenin is subsequently recrystallised in pharmaceutical or edible grade from the said form VII material using an anhydrous IPA-compatible organic solvent such as acetone, which does not form a solvate with smilagenin. It is further preferred that at no stage in the preparation or purification of the smilagenin, including the stage of formation of any form VII material or other intermediate form of smilagenin, is it necessary (or done) to remove water from the smilagenin, or from any mixture containing it, using a solid hygroscopic material such as magnesium sulphate.

Examples 2, 6 and 7 of WO-A-2004/037845 describe certain laboratory scale batchwise procedures for purifying smilagenin via recrystallisation from iso-propyl alcohol (2-propanol). However, in none of these Examples is it stated that the precipitated material is an IPA solvate of smilagenin, let alone a hemi-IPA solvate. To the extent that it may be necessary in any jurisdiction to exclude the disclosures of those examples and subject-matter that is obvious therefrom from the scope of protection for the form VII material, processes for its preparation, and uses thereof, such disclosures—and especially the disclosures of the purification of the initial impure smilagenin using iso-propyl alcohol—are hereby disclaimed from the present application. In particular, in such jurisdictions the form VII material according to the present invention may comprise the form VIII material in substantially pure isolated form prepared on a kilogram scale. As mentioned above, this material is precipitated from the reduced IPA solution after azeotropic distillation and can conveniently be recrystallised as pharmaceutical or edible grade anhydrous unsolvated smilagenin (e.g. in form I or form III, e.g. in substantially pure isolated form prepared on a kilogram scale) using an anhydrous IPA-compatible organic solvent such as acetone, which does not form a solvate with smilagenin.

Amorphous Form

The amorphous form is non-crystalline. We have found that amorphous smilagenin appears to have potentially useful water-solubility and stability with respect to conversion to a crystal form. These characteristics offer improved manufacture, formulation, storage and bioavailability of smilagenin in comparison with the prior art crystalline form.

The amorphous smilagenin we have prepared has an XRPD pattern which shows no peaks that would be characteristic of any crystalline structure.

Derivatives

The term “derivatives” used herein refers particularly to the compounds defined and described in the prior art patent documents acknowledged above in relation to the known biological activities of smilagenin (U.S. Pat. No. 3,890,438; U.S. Pat. No. 4,680,289; U.S. Pat. No. 6,258,386; WO-A-01/23406; WO-A-01/23407; WO-A-01/23408; WO-A-01/49703; WO-A-02/079221; and WO-A-03/082893).

Such derivatives include pharmaceutically acceptable pro-drugs of smilagenin and pharmaceutically acceptable salts thereof.

Pro-drugs of smilagenin may especially include 3-position carboxylate esters such as the cathylate (ethoxycarbonyloxy), acetate, succinate, propionate, butyrate, valerate, isovalerate, caproate, isocaproate, diethylacetate, octanoate, decanoate, laurate, myristate, palmitate, stearate, benzoate, phenylacetate, phenylpropionate, cinnamate, p-nitrobenzoyloxy, 3,5-dinitrobenzoyloxy, p-chlorobenzoyloxy, 2,4-dichlorobenzoyloxy, p-bromobenzoyloxy, m-bromobenzoyloxy, p-methoxy-benzoyloxy, phthalyl, glycinate, alaninate, valinate, phenylalaninate, isoleucinate, methioninate, argininate, aspartate, cysteinate, glutaminate, histidinate, lysinate, prolinate, serinate, threoninate, tryptophanate, tyrosinate, fumarate and maleate esters.

“Pharmaceutically acceptable salts” means the relatively non-toxic, inorganic and organic acid addition salts, and base addition salts, of compounds of the present invention. These salts can be prepared in situ during the final isolation and purification of the compounds. In particular, acid addition salts can be prepared by separately reacting the purified compound in its free base form with a suitable organic or inorganic acid and isolating the salt thus formed. See, for example S. M. Berge et al., Pharmaceutical Salts, J. Pharm. Sci., 66: pp. 1-19 (1977) which is incorporated herein by reference. Base addition salts can also be prepared by separately reacting the purified compound in its acid form with a suitable organic or inorganic base and isolating the salt thus formed. Base addition salts include pharmaceutically acceptable metal and amine salts. Examples of suitable acid addition salts are those formed with acids selected from hydrochloric, sulphuric, phosphoric and nitric acids. Examples of suitable base addition salts are those formed with bases selected from sodium hydroxide, potassium hydroxide and ammonium hydroxide.

Medicaments, Foodstuffs, Food Supplements and Beverages

According to the invention, a composition may comprise a material as described above in admixture with one or more further component selected from: one or more other materials as described above, another form of smilagenin, any other biologically active material, and any biologically inactive material.

The composition may be prepared by a method comprising admixing a material as described above with one or more further component selected from: one or more other materials as described above, another form of smilagenin, any other biologically active material, and any biologically inactive material.

According to the invention, the material or the composition (e.g. the medicament, foodstuff, food supplement or beverage) may be used for the treatment of a condition selected from: high blood cholesterol levels, obesity and diabetes obesity syndromes, cognitive dysfunction and allied conditions, non-cognitive neurodegeneration, non-cognitive neuromuscular degeneration, motor-sensory neurodegeneration and loss of receptor function in the absence of cognitive, neural or neuromuscular impairment.

Still further, the invention therefore provides a method of treatment of a human or non-human animal (e.g. a human) suffering from, or susceptible to, a condition selected from: high blood cholesterol levels, obesity and diabetes obesity syndromes, cognitive dysfunction and allied conditions, non-cognitive neurodegeneration, non-cognitive neuromuscular degeneration, motor-sensory neurodegeneration and loss of receptor function in the absence of cognitive, neural or neuromuscular impairment, which comprises administering to the said human or non-human animal an effective amount of a material or composition as described above.

The active agent prepared according to the present invention may thus be formulated into any suitable composition form for administration to a human or non-human animal patient. The composition may consist of the active agent alone or may include the active agent and any suitable additional component, such as one or more pharmaceutically acceptable carriers, diluents, adjuvants, excipients, or vehicles, such as preserving agents, fillers, disintegrating agents, wetting agents, emulsifying agents, suspending agents, sweetening agents, flavoring agents, perfuming agents, antibacterial agents, antifungal agents, lubricating agents and dispensing agents, depending on the nature of the mode of administration and dosage forms.

The composition may, for example, be a pharmaceutical composition (medicament), a foodstuff, food supplement or beverage.

The terms “foodstuff”, “food supplement” and “beverage” used herein have the normal meanings for those terms, and are not restricted to pharmaceutical preparations. The appropriate pharmaceutical or edible grade of ingredients will be used, according to the desired composition form.

For further details of suitable composition forms and dosages, please refer to U.S. Pat. No. 3,890,438, U.S. Pat. No. 4,680,289; U.S. Pat. No. 6,258,386; WO-A-01/23406; WO-A-01/23407; WO-A-01/23408; WO-A-01/49703; WO-A-02/07922; and WO-A-03/082893.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 shows an XRPD pattern (λ=1.5406 Angstroms) obtained from a sample of commercially available smilagenin in crystalline form II (prior art);

FIG. 2 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form I;

FIG. 3 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form III;

FIG. 4 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form IIIA;

FIG. 5 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form V;

FIG. 6 shows a DSC trace of a sample of smilagenin in crystalline form V, shown to be a monohydrate;

FIG. 7 shows a TGA of a sample of smilagenin in crystalline form V, shown to be a monohydrate;

FIG. 8 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form VI (believed to be smilagenin channel hydrate);

FIG. 9 shows a DSC trace of a sample of smilagenin in crystalline form VI;

FIG. 10 shows a TGA of a sample of smilagenin in crystalline form VI;

FIG. 11 shows a vapour sorption graph of a sample of smilagenin in crystalline form VI;

FIG. 12 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin iso-propyl alcohol (IPA)-solvate in crystalline form VII;

FIG. 13 shows a DSC trace of a sample of smilagenin IPA-solvate in crystalline form VII;

FIG. 14 shows a TGA of a sample of smilagenin IPA-solvate in crystalline form VII, shown to be a hemi-TA-solvate;

FIG. 15 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin in crystalline form VI, with significant peaks marked by arrows; and

FIG. 16 shows an XRPD pattern (λ=1.5406 Angstroms) of a sample of smilagenin IPA-solvate in crystalline form VII, with significant peaks are marked by arrows.

EXAMPLES AND DETAILED DESCRIPTION OF THE DRAWINGS

The following non-limiting Examples are provided as further illustration of the present invention, but without limitation, and are discussed with reference to the drawings.

Starting Materials

Samples of commercially available smilagenin were purchased from Research Plus Inc and Steraloids Inc.

The samples were analysed by XRPD and defined as form II by our nomenclature. A sample from Research Plus was examined by DSC and TGA and found to be anhydrous.

Example 1 Crystalline Form I

A. Crystallisation from Acetone

Smilagenin (10.0 g) was suspended in acetone (250 ml) and the mixture heated to reflux. The resultant solution was decanted from some undissolved solids and reheated to reflux to afford a clear solution. The solution was allowed to cool over about 3.5 hours to 29° C. and further cooled with an ice/water batch to 2° C. The resultant solid was harvested by filtration, washed with cold (5° C.) acetone (50 ml) and dried in a vacuum oven for 3 days to afford 7.4 g of pure smilagenin, which was characterised by XRPD as form I under our nomenclature.

B. Crystallisation from Acetonitrile

A suspension of smilagenin (1.05 g) in acetonitrile (10 ml) was stirred at ambient temperature overnight. The solid was harvested by filtration and dried in a vacuum oven at 80° C. to afford smilagenin form I (0.92 g, 88% yield).

Example 2 Crystalline Form II

Smilagenin was manufactured by stereospecific reduction of diosgenin according to the process described in PCT Patent Application No. PCT/GB2003/001780 (WO-A-2004/037845).

The smilagenin was subjected to XRPD and the pattern was found to be substantially similar to that shown in FIG. 1 of the drawings. On this basis, the material was characterised as form II under our nomenclature.

Examples 3 and 4 Crystalline Form III Example 3

Smilagenin (10.0 g) was suspended in acetone (250 ml) and the mixture heated to reflux.

The resultant solution was cooled to 2° C. over about 15 minutes and the solid harvested by filtration, washed with cold (5° C.) acetone (250 ml) and dried in a vacuum oven for about 24 hours to afford 8.1 g of pure smilagenin, which was characterised by XRPD as form III under our nomenclature.

Example 4

Smilagenin (200 mg; form II) was suspended in tert-butyl methyl ether (4 ml) and stirred for about 48 hours. The solid was harvested by filtration and dried to afford 40 mg, which was characterised as form III under our nomenclature by XRPD, DSC and TGA.

Examples 5 to 9 Crystalline Form V Example 5

Water (200 ml) was added to a suspension of smilagenin (20 g) in acetone (200 ml) and the mixture stirred for about 2 hours. The solid was harvested by filtration, dried in a vacuum oven at 40° C. for about 24 hours to afford 20.5 g which was characterised by XRPD as form V under our nomenclature. The water content was determined as 4.4% by Karl Fischer analysis.

Example 6

Smilagenin (200 mg; form II) was suspended in hexane (10 ml) and stirred for about 48 hours. The solid was harvested by filtration and dried to afford 80 mg which was characterised as form V under our nomenclature by XRPD, DSC and TGA.

Example 7

Smilagenin (500 mg; form II) was suspended in tetrahydrofuran (2 ml) and stirred for about 48 hours. The solid was harvested by filtration and dried to afford 80 mg which was characterised as form V under our nomenclature by XRPD, DSC and TGA.

Examples 8 and 9

Smilagenin (Research Plus Inc.) was recrystallised using slurry crystallisation with butanone (Example 8) or 50% aqueous ethanol (Example 9) as the recrystallisation solvent. In each case the recrystallised material was subjected to XRPD and was characterised as a mixture of forms III and V under our nomenclature.

Example 10 Crystalline Form IIIA

Smilagenin (Research Plus Inc) was recrystallised using slurry crystallisation with dimethylformamide as the recrystallisation solvent.

The recrystallised material was subjected to XRPD and on this basis the material was characterised as crystalline form IIIA under our nomenclature.

Example 11 Crystalline Form VI (Smilagenin Channel Hydrate)

Smilagenin (260 mg) was weighed into a round bottomed flask and methanol (10 ml) was added. The contents were heated to 70° C. to affect complete dissolution, allowed to cool to room temperature and stirred at room temperature for 60 minutes. The solid was collected by filtration and air dried for about 2.5 hours.

The X-ray powder diffraction pattern is shown in FIG. 8, the differential scanning calorimetry trace is shown in FIG. 9 and the thermogravimetric analysis is shown in FIG. 10.

The DSC trace shows a weak broad endothermic transition up to 50° C., an exothermic transition at 120° C. followed by a final high energy melting transition at 188° C. TGA analysis confirms that the initial endotherm is associated with loss of water and that the transition at 121° C. is not associated with any solvent loss. Analysis of the sample by Karl Fischer titration confirmed that the solvent was water.

Vapour sorption studies (see FIG. 11) show that the sample is hygroscopic and adsorbs up to 9% water (about 2 mol. eq. water; i.e. a dihydrate) at high humidity and reversibly loses the water at low humidity. This suggests that this form is a channel hydrate of variable smilagenin:water stoichiometry, depending on the surrounding temperature and humidity.

Example 12 Crystalline Form VII (Smilagenin IPA-Solvate)

Smilagenin (150 mg) was added to iso-propyl alcohol (IPA) (5 ml) and the mixture heated to 70° C. to ensure dissolution. The clear solution was then allowed to cool to 40° C. over 2 hours, whereupon sudden precipitation occurred. The mixture was re-heated to 65° C. to dissolve the material and the solution re-cooled to 45° C., held at 45° C. for 15 minutes, cooled to 40° C., and held at 40° C. for 2 hours. The slurry was then cooled to room temperature and aged over a weekend at room temperature. After this time the solid was collected by filtration and air dried for about 3 hours.

The X-ray powder diffraction pattern is shown in FIG. 12, the differential scanning calorimetry trace is shown in FIG. 13 and the thermogravimetric analysis is shown in FIG. 14.

The DSC shows a broad endotherm between 40° C. and 140° C. that is consistent with loss of IPA from the sample. This is confirmed by TGA analysis which indicates 6.3% IPA present in the sample which is consistent with a hemi-IPA solvate of smilagenin. The IPA appears to be loosely bound in the crystal as it is lost from about 40° C. upwards in the DSC.

Example 13 Amorphous Smilagenin

Smilagenin (10 g) was heated to its melt using a temperature controlled heating mantle and held until a complete molten liquid was formed. The molten mass was poured into a Dewar containing approximately 150 ml of liquid nitrogen. The sample was decanted into a glass beaker and the liquid nitrogen allowed to evaporate. The sample was then transferred to a glass vial, flushed with dry nitrogen and then sealed. The sample was characterised as amorphous smilagenin on the basis of the XRPD pattern, which showed a lack of significant diffraction lines.

TABLE A XRPD Intensities for Smilagenin Crystal Forms I, II, III and V (λ = 1.5406 Angstroms) at regularly spaced intervals in the 2-theta Range 5 to 50 degrees λ = 1.5406 Å Degrees (2θ) Form I Form II Form III Form V 5 225 174 384 231 5.02 231 154 404 204 5.04 231 159 384 193 5.06 228 185 380 240 5.08 225 177 365 199 5.1 199 172 392 225 5.12 210 202 365 188 5.14 199 172 428 222 5.16 213 188 392 207 5.18 169 207 396 210 5.2 185 164 357 213 5.22 216 196 404 216 5.24 174 185 350 193 5.26 196 188 420 213 5.28 156 177 396 213 5.3 216 202 361 231 5.32 185 180 396 202 5.34 207 188 396 216 5.36 207 202 372 234 5.38 216 190 369 234 5.4 228 185 400 216 5.42 188 193 369 231 5.44 185 193 365 207 5.46 190 228 342 246 5.48 196 222 376 228 5.5 246 207 372 256 5.52 193 199 458 262 5.54 202 216 346 279 5.56 202 185 357 262 5.58 222 228 361 339 5.6 196 262 350 306 5.62 210 219 369 335 5.64 202 279 357 353 5.66 207 250 365 372 5.68 199 256 324 404 5.7 204 256 346 392 5.72 199 256 372 484 5.74 204 282 350 520 5.76 210 335 392 511 5.78 222 317 380 620 5.8 231 412 353 756 5.82 210 441 357 864 5.84 190 458 353 1116 5.86 253 471 342 1347 5.88 222 471 388 1529 5.9 193 372 342 1731 5.92 193 174 365 1576 5.94 196 177 384 918 5.96 210 172 396 424 5.98 199 146 380 231 6 202 161 365 243 6.02 193 146 369 185 6.04 213 185 400 177 6.06 196 149 392 174 6.08 216 139 424 159 6.1 216 149 428 159 6.12 272 169 449 154 6.14 240 128 462 174 6.16 219 237 467 180 6.18 210 151 506 182 6.2 250 164 502 154 6.22 289 156 529 154 6.24 262 149 552 154 6.26 246 137 543 154 6.28 272 154 424 156 6.3 269 128 380 177 6.32 272 174 342 185 6.34 259 164 313 164 6.36 310 117 369 146 6.38 313 137 324 128 6.4 331 159 320 161 6.42 384 137 339 146 6.44 365 137 350 156 6.46 384 144 299 135 6.48 437 151 339 151 6.5 467 151 335 146 6.52 543 137 317 139 6.54 590 137 328 166 6.56 600 144 361 146 6.58 751 142 372 159 6.6 864 142 335 142 6.62 986 156 328 154 6.64 1116 156 346 169 6.66 1274 151 335 177 6.68 1274 135 396 137 6.7 1190 146 388 159 6.72 1183 159 328 151 6.74 1325 182 376 159 6.76 1747 123 412 132 6.78 2070 132 380 151 6.8 2470 137 365 159 6.82 3226 137 380 149 6.84 3192 149 441 135 6.86 4122 144 424 130 6.88 6906 149 416 180 6.9 6939 161 449 144 6.92 4638 166 506 164 6.94 2162 151 520 159 6.96 718 139 515 161 6.98 342 161 576 169 7 310 135 566 151 7.02 272 132 640 151 7.04 259 146 671 123 7.06 250 154 745 139 7.08 276 146 801 132 7.1 256 128 858 139 7.12 237 114 847 144 7.14 269 128 1076 154 7.16 266 144 1082 159 7.18 259 137 1190 132 7.2 246 139 1267 146 7.22 234 149 1225 146 7.24 225 130 1043 156 7.26 213 137 740 144 7.28 185 128 534 154 7.3 174 142 400 139 7.32 164 146 369 164 7.34 180 114 380 172 7.36 166 151 313 169 7.38 164 128 342 146 7.4 172 142 286 123 7.42 169 135 313 139 7.44 146 154 299 154 7.46 169 142 289 139 7.48 164 144 296 149 7.5 164 117 306 159 7.52 151 128 286 156 7.54 166 142 299 169 7.56 154 154 303 144 7.58 144 130 299 119 7.6 128 156 292 144 7.62 154 156 289 154 7.64 164 117 286 139 7.66 146 144 269 144 7.68 137 121 256 144 7.7 159 169 286 161 7.72 149 144 269 142 7.74 161 164 266 166 7.76 132 125 266 139 7.78 151 112 282 130 7.8 161 130 289 149 7.82 156 128 269 151 7.84 142 161 299 139 7.86 166 128 272 149 7.88 135 139 276 146 7.9 139 142 269 142 7.92 128 144 266 159 7.94 132 130 256 172 7.96 210 144 276 161 7.98 128 146 279 151 8 146 128 292 146 8.02 146 130 253 137 8.04 151 137 299 159 8.06 259 119 256 161 8.08 125 121 276 154 8.1 142 123 276 156 8.12 128 135 292 142 8.14 149 139 289 137 8.16 177 123 253 137 8.18 135 139 299 137 8.2 130 121 272 144 8.22 121 137 262 172 8.24 100 106 262 139 8.26 213 119 266 132 8.28 144 110 276 139 8.3 130 117 279 128 8.32 135 112 269 137 8.34 139 130 266 135 8.36 177 130 216 137 8.38 128 130 296 144 8.4 139 132 279 123 8.42 125 92 282 125 8.44 125 112 272 154 8.46 114 121 256 135 8.48 303 130 262 137 8.5 114 117 289 142 8.52 119 128 256 139 8.54 149 110 282 125 8.56 132 121 289 188 8.58 119 132 279 142 8.6 110 128 243 121 8.62 106 98 272 137 8.64 110 130 289 159 8.66 125 117 313 128 8.68 125 117 299 114 8.7 114 104 303 313 8.72 135 128 317 132 8.74 121 125 303 135 8.76 112 128 306 121 8.78 112 130 313 112 8.8 130 106 320 135 8.82 119 142 350 151 8.84 119 125 320 137 8.86 114 144 259 142 8.88 117 142 286 146 8.9 130 156 303 130 8.92 139 137 269 164 8.94 137 149 262 144 8.96 110 182 262 164 8.98 142 144 292 154 9 119 151 282 137 9.02 135 154 269 166 9.04 130 159 262 207 9.06 130 161 286 169 9.08 149 188 279 199 9.1 137 188 303 202 9.12 144 199 313 210 9.14 130 210 306 225 9.16 130 210 292 222 9.18 144 216 286 219 9.2 149 253 303 250 9.22 142 222 313 225 9.24 149 276 313 276 9.26 164 310 328 269 9.28 193 335 310 303 9.3 182 369 357 342 9.32 182 392 392 361 9.34 188 441 380 433 9.36 228 511 400 388 9.38 213 543 408 449 9.4 246 529 462 502 9.42 250 625 428 557 9.44 213 635 506 625 9.46 210 600 480 600 9.48 199 562 562 605 9.5 219 372 557 586 9.52 210 250 635 471 9.54 202 172 595 384 9.56 207 125 620 222 9.58 180 108 493 169 9.6 182 125 454 128 9.62 130 100 376 146 9.64 149 94 282 135 9.66 137 121 299 130 9.68 121 112 259 128 9.7 135 104 282 98 9.72 119 100 286 119 9.74 125 108 228 117 9.76 123 92 272 119 9.78 123 96 292 137 9.8 108 108 250 98 9.82 110 102 276 106 9.84 119 83 286 108 9.86 125 79 276 98 9.88 123 137 292 106 9.9 112 98 256 108 9.92 114 102 262 106 9.94 121 88 272 106 9.96 123 86 262 112 9.98 119 98 279 123 10 119 106 282 94 10.02 96 98 250 98 10.04 130 108 286 117 10.06 144 112 266 102 10.08 125 108 269 108 10.1 146 108 289 83 10.12 125 102 256 125 10.14 146 114 292 106 10.16 132 121 289 104 10.18 142 108 286 114 10.2 156 94 282 125 10.22 164 130 269 123 10.24 169 104 256 98 10.26 154 102 286 114 10.28 182 100 286 110 10.3 172 102 292 125 10.32 161 90 286 94 10.34 172 79 269 102 10.36 204 313 276 102 10.38 219 164 266 94 10.4 240 96 289 96 10.42 225 92 306 100 10.44 188 90 292 110 10.46 219 81 306 119 10.48 234 86 262 106 10.5 266 79 292 98 10.52 279 100 272 106 10.54 320 88 317 108 10.56 346 108 262 96 10.58 353 100 303 106 10.6 428 76 303 112 10.62 590 108 324 112 10.64 812 102 372 119 10.66 888 100 303 100 10.68 745 96 286 100 10.7 681 92 289 110 10.72 671 100 292 98 10.74 818 108 299 117 10.76 1050 102 339 108 10.78 1116 112 353 125 10.8 1005 96 357 137 10.82 853 92 384 144 10.84 812 110 437 132 10.86 484 94 376 139 10.88 328 96 420 104 10.9 250 121 437 161 10.92 256 102 433 154 10.94 289 121 408 144 10.96 269 135 458 172 10.98 335 132 506 172 11 339 142 552 144 11.02 372 137 515 185 11.04 303 161 586 207 11.06 213 135 640 190 11.08 144 185 666 240 11.1 128 177 708 234 11.12 202 188 708 306 11.14 112 199 713 292 11.16 119 228 724 328 11.18 110 199 676 317 11.2 119 237 620 396 11.22 125 253 557 408 11.24 112 225 467 400 11.26 132 204 420 433 11.28 130 204 365 445 11.3 130 231 365 441 11.32 132 237 324 350 11.34 123 207 328 433 11.36 125 276 324 441 11.38 139 246 289 493 11.4 139 310 320 506 11.42 149 276 296 610 11.44 146 346 342 645 11.46 154 350 310 708 11.48 139 372 331 824 11.5 169 445 335 955 11.52 161 488 306 1089 11.54 207 524 335 1225 11.56 204 610 335 1414 11.58 207 702 313 1544 11.6 237 756 324 1840 11.62 225 847 310 2200 11.64 296 992 313 2694 11.66 328 1239 328 3434 11.68 335 1521 335 3844 11.7 250 1962 342 4173 11.72 256 2275 365 4651 11.74 188 1656 369 6147 11.76 161 870 420 7006 11.78 121 369 392 5227 11.8 149 193 384 2714 11.82 154 137 388 992 11.84 151 104 404 441 11.86 154 123 437 299 11.88 139 114 445 234 11.9 144 112 471 169 11.92 142 86 511 182 11.94 149 121 511 154 11.96 177 102 471 164 11.98 159 108 538 146 12 169 102 566 123 12.02 132 88 511 142 12.04 169 102 615 114 12.06 180 96 676 104 12.08 190 106 676 98 12.1 182 110 702 108 12.12 166 77 801 100 12.14 182 94 824 106 12.16 210 83 900 104 12.18 250 83 1018 104 12.2 231 79 1082 117 12.22 279 83 1204 100 12.24 269 92 1246 98 12.26 259 74 1362 92 12.28 324 77 1429 100 12.3 353 102 1560 98 12.32 376 98 1632 110 12.34 445 85 1714 108 12.36 428 92 1689 94 12.38 462 79 1722 108 12.4 420 98 1624 100 12.42 437 100 1592 108 12.44 497 92 1513 100 12.46 562 83 1296 104 12.48 676 90 1190 110 12.5 615 94 1096 90 12.52 635 110 1037 94 12.54 557 102 1024 102 12.56 497 102 986 123 12.58 488 117 980 128 12.6 493 98 924 119 12.62 497 108 936 106 12.64 400 108 1037 130 12.66 339 102 992 108 12.68 289 108 1050 144 12.7 262 92 1204 117 12.72 272 108 1260 256 12.74 303 102 1376 132 12.76 313 119 1513 121 12.78 328 132 1656 110 12.8 380 114 1747 98 12.82 353 135 1849 125 12.84 396 142 2153 121 12.86 388 117 2352 128 12.88 408 144 2570 121 12.9 562 128 2809 123 12.92 467 114 3025 128 12.94 529 146 3387 121 12.96 581 130 3516 114 12.98 534 154 3906 137 13 630 149 4238 135 13.02 581 142 4225 137 13.04 640 142 3881 151 13.06 610 166 3469 135 13.08 671 190 2894 132 13.1 660 146 2228 151 13.12 681 190 1927 172 13.14 718 199 1875 156 13.16 773 219 1823 164 13.18 894 213 1875 182 13.2 999 262 1998 222 13.22 1163 306 2237 262 13.24 1239 276 2343 228 13.26 1318 328 2530 228 13.28 1362 331 2725 228 13.3 1529 369 2841 240 13.32 1673 396 3069 262 13.34 1789 424 3329 279 13.36 1840 502 3457 282 13.38 2034 524 3672 292 13.4 2285 524 3697 350 13.42 2381 605 3528 376 13.44 2460 605 3493 396 13.46 2560 713 3505 380 13.48 2704 650 3341 424 13.5 2560 708 3341 462 13.52 2490 697 3457 467 13.54 2034 724 3446 529 13.56 1989 835 3318 548 13.58 2088 778 3181 581 13.6 2304 801 2884 590 13.62 2746 807 2520 655 13.64 3457 686 2247 610 13.66 3672 581 2162 576 13.68 3469 445 2125 497 13.7 3612 433 2247 416 13.72 3807 428 2294 392 13.74 4436 433 2372 320 13.76 5580 437 2470 324 13.78 7362 441 2621 317 13.8 10547 557 2756 331 13.82 10424 534 2798 361 13.84 7762 620 2841 380 13.86 4900 751 2809 357 13.88 2172 807 2714 458 13.9 1176 930 2601 511 13.92 778 1018 2314 562 13.94 650 1176 1945 610 13.96 718 1376 1665 729 13.98 702 1537 1296 734 14 745 1884 1176 900 14.02 724 2181 1037 949 14.04 740 2372 1011 1018 14.06 773 2673 1011 1163 14.08 894 3036 1043 1354 14.1 876 3411 1043 1490 14.12 936 3721 1211 1632 14.14 1024 4032 1218 1781 14.16 1082 4624 1318 2007 14.18 1076 4679 1421 2209 14.2 1170 5170 1490 2304 14.22 1163 5213 1764 2591 14.24 1142 5098 1772 2611 14.26 1050 4665 1892 2735 14.28 912 4199 2079 2735 14.3 724 3192 2266 2440 14.32 625 2098 2352 2061 14.34 497 1318 2500 1640 14.36 449 818 2746 1354 14.38 433 595 2884 1109 14.4 441 590 3025 818 14.42 484 600 3170 745 14.44 408 605 3283 778 14.46 480 702 3204 858 14.48 408 650 3047 930 14.5 404 740 2530 1109 14.52 445 734 2088 1102 14.54 376 784 1697 1183 14.56 339 876 1384 1310 14.58 396 924 1318 1399 14.6 372 906 1310 1490 14.62 328 858 1289 1482 14.64 328 681 1296 1296 14.66 250 471 1354 1089 14.68 286 331 1325 795 14.7 299 256 1436 571 14.72 310 279 1482 350 14.74 306 228 1600 256 14.76 292 243 1697 199 14.78 296 262 1731 188 14.8 331 272 1927 204 14.82 339 306 1989 222 14.84 369 317 2125 204 14.86 388 380 2352 240 14.88 449 412 2460 262 14.9 484 408 2601 262 14.92 571 420 2756 279 14.94 605 449 2970 262 14.96 713 449 3181 289 14.98 740 502 3283 328 15 900 511 3226 339 15.02 992 497 3260 342 15.04 1043 488 3329 320 15.06 1089 484 3552 353 15.08 1156 484 3493 365 15.1 1267 471 3624 372 15.12 1444 484 3931 380 15.14 1632 538 4147 408 15.16 1537 511 4083 392 15.18 1592 524 4382 433 15.2 1697 484 4436 369 15.22 1608 493 4382 404 15.24 1498 475 4122 342 15.26 1340 493 3931 350 15.28 1102 515 3457 420 15.3 918 600 2767 400 15.32 697 615 2362 437 15.34 660 724 1971 449 15.36 566 795 1731 506 15.38 600 882 1706 571 15.4 586 1063 1537 635 15.42 635 1183 1544 708 15.44 702 1362 1584 930 15.46 790 1467 1444 1018 15.48 807 1616 1399 1089 15.5 876 1884 1362 1211 15.52 882 2162 1369 1310 15.54 942 2266 1406 1391 15.56 1063 2460 1362 1616 15.58 1142 2735 1310 1858 15.6 1267 3025 1406 1936 15.62 1332 3125 1421 2190 15.64 1310 3238 1444 2352 15.66 1282 3295 1498 2470 15.68 1197 3249 1467 2570 15.7 1050 3114 1560 2540 15.72 1024 3058 1560 2550 15.74 1109 3014 1656 2652 15.76 1030 3114 1673 2809 15.78 1089 3047 1632 3102 15.8 1030 2894 1608 3283 15.82 1037 2520 1537 3014 15.84 961 1884 1436 2611 15.86 949 1225 1475 2116 15.88 973 734 1498 1537 15.9 942 400 1568 1063 15.92 894 259 1616 681 15.94 1030 219 1722 392 15.96 1050 199 1789 246 15.98 1096 161 1849 193 16 1037 185 1910 199 16.02 894 159 1962 169 16.04 692 164 2025 164 16.06 502 144 2007 196 16.08 416 130 1901 154 16.1 350 144 1849 174 16.12 310 137 1600 132 16.14 256 137 1544 151 16.16 269 121 1325 216 16.18 237 146 1197 130 16.2 269 151 1122 135 16.22 259 151 1136 149 16.24 256 161 1142 137 16.26 243 161 1260 144 16.28 303 151 1232 159 16.3 282 199 1414 161 16.32 313 188 1505 151 16.34 328 174 1592 177 16.36 320 234 1714 213 16.38 331 262 1875 202 16.4 361 299 1989 219 16.42 384 303 2200 210 16.44 361 292 2372 240 16.46 376 339 2725 266 16.48 420 342 2767 306 16.5 400 365 2992 313 16.52 449 396 3238 331 16.54 424 428 3422 342 16.56 471 428 3636 342 16.58 420 475 3697 365 16.6 424 428 3576 384 16.62 353 488 3295 412 16.64 339 529 2873 412 16.66 353 548 2673 408 16.68 339 543 2611 428 16.7 328 543 2652 437 16.72 313 557 2500 467 16.74 292 502 2500 441 16.76 317 449 2632 416 16.78 313 538 2683 380 16.8 296 529 2510 369 16.82 350 566 2530 396 16.84 350 605 2343 384 16.86 331 660 2070 404 16.88 369 671 1798 462 16.9 420 734 1459 538 16.92 420 762 1253 600 16.94 416 795 1129 590 16.96 454 882 1056 702 16.98 493 980 1030 729 17 538 1050 906 888 17.02 557 1274 949 955 17.04 548 1310 942 1056 17.06 571 1537 955 1197 17.08 620 1608 980 1303 17.1 630 1892 930 1459 17.12 671 2016 986 1568 17.14 801 2190 1050 1764 17.16 847 2480 1030 1971 17.18 900 2560 1043 2134 17.2 912 2673 1102 2381 17.22 967 2938 1102 2735 17.24 1030 2873 1129 2809 17.26 999 2894 1082 2916 17.28 1005 2591 1122 2809 17.3 1050 2088 1082 2470 17.32 942 1421 986 2285 17.34 955 858 1011 1927 17.36 949 534 1018 1429 17.38 1037 353 961 853 17.4 1218 269 924 590 17.42 1482 210 918 380 17.44 1781 185 999 250 17.46 1980 154 955 250 17.48 1962 169 1056 253 17.5 2043 169 1030 240 17.52 1989 169 1037 286 17.54 1866 174 1018 276 17.56 2162 219 1122 313 17.58 2218 219 1142 286 17.6 2088 240 1190 320 17.62 2275 190 1190 388 17.64 2694 174 1183 433 17.66 2611 144 1082 376 17.68 2430 154 1037 272 17.7 2323 123 999 253 17.72 2266 128 930 180 17.74 2266 128 942 119 17.76 2007 161 973 121 17.78 1927 117 918 149 17.8 1163 135 936 135 17.82 829 132 1018 149 17.84 506 139 1063 137 17.86 396 139 1136 154 17.88 376 180 1218 151 17.9 380 190 1332 137 17.92 493 185 1406 159 17.94 400 180 1444 190 17.96 376 182 1568 159 17.98 412 174 1640 204 18 412 164 1756 196 18.02 428 210 1866 180 18.04 433 286 2043 190 18.06 396 216 2034 216 18.08 353 196 2079 222 18.1 372 222 2052 213 18.12 320 182 1823 213 18.14 328 172 1640 202 18.16 246 154 1414 196 18.18 234 137 1156 149 18.2 246 132 936 177 18.22 222 151 801 146 18.24 237 130 740 159 18.26 216 121 630 164 18.28 253 144 625 164 18.3 262 154 640 182 18.32 213 180 655 161 18.34 225 166 671 199 18.36 228 188 692 207 18.38 225 185 692 225 18.4 272 185 745 246 18.42 256 253 745 276 18.44 269 250 778 269 18.46 250 282 745 320 18.48 269 331 829 324 18.5 317 372 876 388 18.52 282 392 900 408 18.54 339 480 924 420 18.56 369 502 961 515 18.58 369 562 924 581 18.6 404 615 1024 660 18.62 428 702 1037 713 18.64 441 724 1011 784 18.66 506 778 942 864 18.68 520 790 924 980 18.7 581 936 870 1156 18.72 620 980 795 1142 18.74 734 1005 724 1260 18.76 724 967 666 1176 18.78 692 992 605 1176 18.8 790 955 635 1136 18.82 864 864 576 1122 18.84 900 835 534 1063 18.86 900 818 529 961 18.88 900 692 538 870 18.9 847 543 543 762 18.92 858 376 511 620 18.94 853 289 529 497 18.96 864 369 534 369 18.98 900 166 557 231 19 864 130 586 196 19.02 912 112 586 144 19.04 1122 117 586 130 19.06 1282 90 595 132 19.08 1429 98 640 102 19.1 1436 104 640 112 19.12 1310 128 650 100 19.14 1218 98 671 130 19.16 1190 112 676 114 19.18 1296 85 686 106 19.2 1616 104 666 119 19.22 1475 112 655 114 19.24 1149 108 581 135 19.26 1043 128 543 117 19.28 773 130 576 114 19.3 562 142 543 110 19.32 488 128 557 117 19.34 458 121 590 106 19.36 380 142 600 132 19.38 380 166 615 128 19.4 384 174 566 144 19.42 408 151 686 130 19.44 424 169 713 146 19.46 441 199 778 154 19.48 441 188 773 164 19.5 506 180 745 154 19.52 484 180 801 174 19.54 534 185 773 144 19.56 671 202 762 149 19.58 625 196 740 161 19.6 552 213 692 169 19.62 686 234 713 210 19.64 751 196 660 185 19.66 762 210 630 199 19.68 864 219 620 199 19.7 1089 188 650 207 19.72 1163 202 666 213 19.74 1170 228 692 207 19.76 1414 253 620 262 19.78 1739 246 645 279 19.8 1632 246 625 253 19.82 1576 262 595 292 19.84 1475 272 625 306 19.86 1467 246 576 259 19.88 1498 225 534 276 19.9 1376 266 600 246 19.92 1096 256 543 207 19.94 692 292 645 190 19.96 524 259 650 219 19.98 441 372 660 240 20 292 400 610 246 20.02 266 404 718 262 20.04 256 471 708 253 20.06 313 515 734 331 20.08 339 562 767 380 20.1 306 571 790 392 20.12 320 671 847 420 20.14 328 702 858 441 20.16 350 829 829 515 20.18 353 853 888 467 20.2 331 930 829 576 20.22 372 900 751 543 20.24 369 1030 745 615 20.26 392 1018 676 681 20.28 424 1056 620 671 20.3 416 986 640 713 20.32 420 1005 586 702 20.34 408 818 610 692 20.36 416 686 640 615 20.38 384 488 655 511 20.4 372 353 600 471 20.42 380 296 713 339 20.44 388 222 645 279 20.46 357 190 630 231 20.48 376 154 620 180 20.5 372 161 600 164 20.52 365 156 600 154 20.54 384 172 552 144 20.56 484 182 586 166 20.58 433 210 493 151 20.6 441 185 538 156 20.62 471 199 529 193 20.64 458 231 488 185 20.66 548 246 488 190 20.68 650 289 543 202 20.7 697 276 475 210 20.72 812 306 475 246 20.74 980 353 506 279 20.76 1204 350 520 276 20.78 955 424 529 303 20.8 986 437 586 317 20.82 812 475 595 335 20.84 538 520 562 412 20.86 529 600 605 437 20.88 449 676 650 524 20.9 404 686 686 511 20.92 400 713 676 576 20.94 433 767 740 650 20.96 433 829 762 713 20.98 462 773 824 713 21 467 807 767 713 21.02 449 745 870 729 21.04 420 713 847 686 21.06 404 640 882 660 21.08 376 620 888 676 21.1 342 595 870 620 21.12 350 543 847 615 21.14 324 576 778 605 21.16 350 615 745 702 21.18 369 630 655 756 21.2 380 645 615 818 21.22 361 660 524 955 21.24 339 666 543 1011 21.26 296 581 515 1076 21.28 262 562 511 967 21.3 246 412 520 824 21.32 240 365 511 692 21.34 202 262 484 548 21.36 219 222 524 392 21.38 188 185 562 324 21.4 207 159 590 234 21.42 199 139 590 169 21.44 199 128 620 159 21.46 199 144 562 144 21.48 231 144 620 139 21.5 182 119 625 130 21.52 202 151 666 159 21.54 174 125 660 130 21.56 207 142 660 123 21.58 196 112 740 123 21.6 237 154 724 139 21.62 213 139 650 149 21.64 193 125 708 137 21.66 213 110 751 135 21.68 213 119 795 132 21.7 213 114 756 128 21.72 272 137 734 159 21.74 276 174 734 132 21.76 286 151 702 142 21.78 286 169 686 166 21.8 306 174 640 144 21.82 289 182 620 174 21.84 306 213 605 219 21.86 289 225 557 216 21.88 324 306 576 234 21.9 342 276 590 276 21.92 412 299 640 286 21.94 433 331 615 282 21.96 462 350 686 353 21.98 515 376 660 433 22 515 433 702 454 22.02 586 480 640 445 22.04 708 625 697 529 22.06 686 562 762 534 22.08 992 625 734 586 22.1 1170 630 713 671 22.12 1459 697 724 778 22.14 1303 767 708 870 22.16 999 795 692 864 22.18 812 858 708 912 22.2 645 900 671 1024 22.22 458 955 666 1050 22.24 313 900 734 1037 22.26 306 835 773 942 22.28 269 660 778 894 22.3 246 595 773 801 22.32 243 484 807 635 22.34 240 454 835 524 22.36 250 437 795 428 22.38 246 420 841 400 22.4 243 404 894 384 22.42 276 441 824 365 22.44 222 346 894 380 22.46 246 335 942 342 22.48 234 361 942 331 22.5 202 237 1076 350 22.52 222 210 1050 259 22.54 216 180 1018 250 22.56 210 161 1096 210 22.58 199 151 1018 185 22.6 182 121 986 196 22.62 151 112 980 159 22.64 164 125 882 161 22.66 177 110 807 166 22.68 193 144 734 159 22.7 196 146 630 159 22.72 188 123 557 174 22.74 188 125 605 146 22.76 246 121 515 172 22.78 193 159 497 154 22.8 256 174 493 149 22.82 243 146 529 190 22.84 246 164 484 174 22.86 250 174 488 182 22.88 262 188 467 193 22.9 279 164 454 190 22.92 282 185 454 253 22.94 299 210 445 237 22.96 303 204 437 256 22.98 317 199 412 276 23 306 216 424 310 23.02 384 269 467 303 23.04 365 246 416 331 23.06 342 289 471 388 23.08 361 282 445 428 23.1 292 313 458 502 23.12 313 384 484 543 23.14 243 365 538 520 23.16 210 376 562 562 23.18 180 384 524 615 23.2 196 342 557 595 23.22 240 306 586 600 23.24 199 346 630 620 23.26 199 317 605 630 23.28 202 296 635 605 23.3 216 289 681 600 23.32 240 286 635 640 23.34 210 339 645 676 23.36 207 350 666 734 23.38 225 396 708 824 23.4 222 388 697 847 23.42 237 416 650 961 23.44 243 543 635 1082 23.46 240 571 635 1267 23.48 286 745 620 1391 23.5 292 1109 615 1490 23.52 310 1354 552 1640 23.54 286 1069 529 1849 23.56 292 762 467 2209 23.58 313 681 445 2052 23.6 282 475 437 1225 23.62 286 299 428 1122 23.64 328 243 420 900 23.66 346 234 424 475 23.68 361 216 480 328 23.7 350 213 441 253 23.72 342 219 458 243 23.74 372 210 475 256 23.76 400 222 506 250 23.78 408 210 506 350 23.8 384 196 484 222 23.82 357 164 506 188 23.84 306 164 484 204 23.86 253 166 480 196 23.88 246 139 462 161 23.9 240 117 433 151 23.92 174 96 376 123 23.94 154 106 372 132 23.96 132 110 388 132 23.98 174 92 357 119 24 142 96 392 125 24.02 139 104 350 154 24.04 144 90 353 100 24.06 166 112 380 128 24.08 123 85 357 135 24.1 137 98 328 114 24.12 149 123 369 128 24.14 139 125 357 119 24.16 159 112 384 149 24.18 130 135 400 144 24.2 164 135 372 159 24.22 164 144 404 164 24.24 177 177 372 164 24.26 172 185 369 193 24.28 207 161 388 188 24.3 164 222 408 234 24.32 182 216 365 207 24.34 188 234 392 253 24.36 196 225 467 276 24.38 216 256 388 361 24.4 213 262 475 335 24.42 207 286 428 342 24.44 222 286 445 369 24.46 253 313 515 396 24.48 216 342 506 396 24.5 231 400 475 471 24.52 253 380 493 467 24.54 286 424 520 538 24.56 237 428 511 515 24.58 256 467 524 497 24.6 286 462 506 529 24.62 339 357 552 576 24.64 299 388 538 552 24.66 259 286 511 462 24.68 234 289 538 433 24.7 193 246 581 335 24.72 172 213 562 269 24.74 172 196 557 199 24.76 169 196 625 225 24.78 172 193 655 202 24.8 161 216 645 193 24.82 159 199 605 188 24.84 166 199 666 190 24.86 174 225 650 210 24.88 169 222 615 228 24.9 161 272 581 250 24.92 159 259 552 231 24.94 159 213 506 222 24.96 159 256 462 188 24.98 156 213 462 213 25 174 180 454 199 25.02 169 172 420 202 25.04 193 161 416 172 25.06 207 164 404 159 25.08 193 135 467 149 25.1 213 144 458 151 25.12 234 130 441 146 25.14 202 121 480 121 25.16 199 125 445 110 25.18 202 149 480 117 25.2 193 112 458 121 25.22 228 106 467 130 25.24 185 112 493 339 25.26 202 112 471 108 25.28 225 128 484 121 25.3 250 161 502 137 25.32 269 123 524 128 25.34 259 128 524 121 25.36 237 154 493 137 25.38 262 142 529 161 25.4 276 146 581 172 25.42 219 142 571 149 25.44 207 164 571 169 25.46 188 169 557 180 25.48 207 166 590 159 25.5 188 266 529 159 25.52 190 169 471 144 25.54 193 164 475 128 25.56 182 166 449 154 25.58 207 204 445 128 25.6 161 210 420 180 25.62 169 269 400 149 25.64 185 228 412 172 25.66 185 266 372 177 25.68 174 266 404 182 25.7 193 292 328 182 25.72 185 269 346 219 25.74 161 286 342 182 25.76 154 289 346 210 25.78 166 365 331 219 25.8 196 296 331 222 25.82 190 266 331 246 25.84 169 279 342 246 25.86 188 276 306 243 25.88 166 320 313 219 25.9 185 296 328 222 25.92 484 324 279 237 25.94 169 310 279 237 25.96 177 299 299 213 25.98 188 292 310 199 26 159 259 310 204 26.02 161 292 292 207 26.04 177 222 313 202 26.06 154 207 296 177 26.08 149 156 331 164 26.1 169 156 289 135 26.12 144 125 320 130 26.14 139 142 292 132 26.16 114 106 303 146 26.18 144 104 292 114 26.2 135 112 317 110 26.22 144 104 320 123 26.24 142 106 324 117 26.26 164 128 292 144 26.28 164 130 313 132 26.3 177 130 299 125 26.32 180 137 328 142 26.34 196 142 328 135 26.36 225 185 320 202 26.38 279 177 342 161 26.4 310 207 350 188 26.42 306 207 331 159 26.44 342 228 369 164 26.46 335 199 365 169 26.48 353 225 353 174 26.5 331 237 388 166 26.52 369 240 416 185 26.54 372 272 424 222 26.56 454 262 437 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172 475 164 27.5 166 174 458 169 27.52 166 144 428 137 27.54 159 174 433 123 27.56 159 139 400 149 27.58 164 172 420 137 27.6 161 156 384 151 27.62 164 149 361 123 27.64 161 123 361 135 27.66 188 159 384 128 27.68 204 142 396 154 27.7 193 144 392 169 27.72 219 135 404 156 27.74 204 128 420 164 27.76 199 156 441 185 27.78 216 154 412 180 27.8 231 159 441 231 27.82 234 156 428 190 27.84 313 193 506 204 27.86 306 172 502 210 27.88 306 172 515 231 27.9 335 185 511 210 27.92 313 204 511 231 27.94 317 237 562 253 27.96 317 237 548 250 27.98 324 243 600 276 28 303 256 557 320 28.02 306 256 557 303 28.04 269 286 566 282 28.06 243 279 543 342 28.08 231 286 576 372 28.1 219 299 548 369 28.12 210 306 576 342 28.14 219 250 576 388 28.16 202 234 557 361 28.18 199 204 586 306 28.2 225 196 520 243 28.22 161 182 529 202 28.24 177 159 497 188 28.26 169 151 480 188 28.28 210 144 420 177 28.3 222 132 467 161 28.32 202 146 449 137 28.34 237 142 484 142 28.36 256 125 428 142 28.38 234 156 424 114 28.4 234 146 437 130 28.42 286 159 437 142 28.44 306 161 420 174 28.46 339 177 445 135 28.48 310 172 458 166 28.5 303 169 416 169 28.52 276 174 437 159 28.54 259 182 458 156 28.56 256 169 437 149 28.58 240 169 449 174 28.6 216 172 433 161 28.62 231 174 441 149 28.64 237 174 445 185 28.66 234 177 433 161 28.68 259 207 424 144 28.7 213 185 416 169 28.72 180 185 408 144 28.74 169 174 441 139 28.76 159 164 420 144 28.78 159 166 408 144 28.8 144 156 458 151 28.82 174 137 388 117 28.84 149 128 408 125 28.86 144 130 416 117 28.88 149 100 420 119 28.9 151 106 380 117 28.92 156 110 428 108 28.94 132 88 404 144 28.96 159 98 376 123 28.98 199 88 396 123 29 169 119 365 110 29.02 199 104 342 123 29.04 193 144 342 151 29.06 228 117 335 159 29.08 210 130 357 169 29.1 216 132 296 164 29.12 246 137 317 151 29.14 246 151 361 174 29.16 276 159 303 185 29.18 253 182 289 225 29.2 269 182 310 199 29.22 246 172 339 219 29.24 266 196 317 231 29.26 228 207 339 234 29.28 240 202 328 234 29.3 234 225 324 266 29.32 210 228 313 282 29.34 202 243 306 320 29.36 177 266 335 339 29.38 204 286 299 342 29.4 169 320 335 388 29.42 177 292 282 388 29.44 159 335 320 384 29.46 182 313 328 416 29.48 169 339 324 437 29.5 169 353 306 416 29.52 159 306 342 335 29.54 149 306 376 365 29.56 149 279 350 328 29.58 156 324 388 303 29.6 159 303 376 279 29.62 156 269 369 282 29.64 161 276 372 259 29.66 174 303 372 266 29.68 207 250 420 234 29.7 199 320 388 262 29.72 210 276 396 259 29.74 210 299 400 240 29.76 190 328 384 269 29.78 180 269 420 282 29.8 199 339 449 262 29.82 210 269 416 276 29.84 219 276 400 262 29.86 207 276 404 253 29.88 225 228 400 259 29.9 185 234 412 250 29.92 210 213 408 202 29.94 213 216 384 204 29.96 231 196 396 210 29.98 222 177 384 193 30 234 166 365 166 30.02 213 139 372 182 30.04 231 137 376 159 30.06 259 112 384 128 30.08 222 102 376 146 30.1 182 108 357 128 30.12 166 90 384 114 30.14 185 98 357 104 30.16 169 100 365 121 30.18 123 123 353 110 30.2 164 114 346 117 30.22 159 106 320 112 30.24 149 88 357 128 30.26 146 114 339 123 30.28 225 123 365 128 30.3 144 130 339 112 30.32 164 117 357 125 30.34 132 137 365 125 30.36 144 144 376 108 30.38 149 123 350 144 30.4 207 137 328 123 30.42 159 151 365 128 30.44 234 142 361 144 30.46 174 151 376 159 30.48 185 169 380 146 30.5 207 166 380 166 30.52 193 177 342 151 30.54 219 156 376 169 30.56 243 193 365 164 30.58 219 169 353 139 30.6 253 169 404 177 30.62 246 166 335 146 30.64 303 169 408 144 30.66 357 146 365 159 30.68 408 177 365 149 30.7 416 166 376 180 30.72 365 137 353 164 30.74 400 193 372 190 30.76 380 174 404 174 30.78 365 177 437 180 30.8 365 185 412 177 30.82 306 174 412 199 30.84 272 177 380 177 30.86 262 161 416 204 30.88 250 151 471 161 30.9 228 149 445 164 30.92 202 172 462 146 30.94 185 161 458 149 30.96 164 169 437 177 30.98 269 185 441 174 31 182 180 428 144 31.02 193 172 445 169 31.04 207 193 449 185 31.06 216 190 441 166 31.08 234 182 420 164 31.1 228 161 437 154 31.12 190 190 416 154 31.14 202 182 449 169 31.16 282 121 424 159 31.18 279 128 445 144 31.2 276 119 400 137 31.22 237 100 408 142 31.24 234 121 380 121 31.26 231 108 313 123 31.28 250 110 365 132 31.3 193 104 339 104 31.32 240 106 342 119 31.34 222 108 313 110 31.36 196 106 350 114 31.38 190 121 350 125 31.4 204 144 320 119 31.42 161 128 335 164 31.44 202 144 335 135 31.46 188 144 266 159 31.48 177 177 306 216 31.5 159 193 286 207 31.52 185 207 324 210 31.54 166 219 313 225 31.56 166 228 313 259 31.58 174 259 317 269 31.6 177 279 313 292 31.62 182 292 324 303 31.64 213 320 339 310 31.66 207 324 335 310 31.68 213 365 331 331 31.7 207 369 335 404 31.72 240 365 357 416 31.74 228 396 339 502 31.76 243 420 357 497 31.78 237 433 328 502 31.8 231 475 350 534 31.82 231 511 369 502 31.84 210 493 384 520 31.86 199 484 372 605 31.88 225 484 350 586 31.9 210 433 339 590 31.92 210 400 346 506 31.94 228 369 342 497 31.96 199 313 331 441 31.98 210 310 350 384 32 199 253 306 328 32.02 190 196 317 296 32.04 177 216 317 246 32.06 193 182 313 259 32.08 174 180 331 199 32.1 166 185 317 225 32.12 156 190 328 188 32.14 182 190 331 216 32.16 144 207 328 213 32.18 151 207 353 240 32.2 132 188 342 228 32.22 142 216 372 256 32.24 161 225 339 219 32.26 144 259 350 256 32.28 149 266 331 246 32.3 159 240 346 262 32.32 149 256 342 299 32.34 156 253 353 286 32.36 135 246 324 320 32.38 128 243 369 306 32.4 135 250 357 306 32.42 151 204 339 320 32.44 154 188 331 289 32.46 123 188 350 276 32.48 149 234 331 250 32.5 149 204 346 266 32.52 151 231 335 256 32.54 112 204 376 269 32.56 154 199 320 231 32.58 146 174 342 222 32.6 139 169 342 210 32.62 130 154 317 185 32.64 125 144 339 177 32.66 137 174 286 177 32.68 139 169 324 174 32.7 166 196 310 169 32.72 164 204 320 164 32.74 139 154 306 166 32.76 182 174 324 159 32.78 166 182 286 166 32.8 185 216 324 164 32.82 188 210 335 193 32.84 210 222 317 202 32.86 213 228 306 210 32.88 202 256 289 234 32.9 196 282 303 234 32.92 216 289 324 266 32.94 213 289 306 246 32.96 210 306 339 269 32.98 228 313 313 276 33 202 328 306 286 33.02 180 369 324 306 33.04 188 353 296 328 33.06 190 369 292 335 33.08 210 433 310 369 33.1 222 437 299 433 33.12 207 445 286 424 33.14 216 392 289 428 33.16 207 441 310 404 33.18 216 449 313 449 33.2 225 416 299 420 33.22 228 437 296 428 33.24 219 441 272 392 33.26 225 388 292 392 33.28 190 357 303 380 33.3 231 324 317 376 33.32 246 276 335 361 33.34 222 269 331 299 33.36 210 272 335 256 33.38 259 262 339 289 33.4 259 243 335 289 33.42 310 231 339 320 33.44 350 213 376 299 33.46 324 256 376 313 33.48 240 240 372 266 33.5 289 225 400 286 33.52 299 207 365 240 33.54 289 213 400 256 33.56 292 213 392 213 33.58 272 210 404 234 33.6 234 253 412 225 33.62 286 253 424 253 33.64 292 228 449 216 33.66 292 237 400 269 33.68 266 240 441 231 33.7 292 253 420 243 33.72 259 250 449 222 33.74 262 256 480 234 33.76 225 282 462 266 33.78 228 253 506 246 33.8 219 269 471 269 33.82 210 279 471 253 33.84 204 269 493 246 33.86 204 269 488 262 33.88 174 282 484 228 33.9 210 328 449 269 33.92 210 303 471 296 33.94 193 365 441 240 33.96 213 353 396 262 33.98 225 369 400 282 34 240 353 392 292 34.02 222 396 412 365 34.04 246 433 384 339 34.06 259 441 392 350 34.08 303 458 353 412 34.1 272 445 331 408 34.12 286 449 342 372 34.14 276 467 350 408 34.16 272 493 320 428 34.18 279 488 339 428 34.2 282 488 317 433 34.22 266 462 306 449 34.24 272 420 342 454 34.26 272 433 350 428 34.28 272 412 306 388 34.3 240 376 320 388 34.32 262 317 306 369 34.34 246 292 342 331 34.36 246 262 296 296 34.38 266 237 353 262 34.4 240 216 292 237 34.42 296 196 317 234 34.44 199 199 331 216 34.46 190 185 353 196 34.48 202 202 339 185 34.5 204 182 339 188 34.52 210 177 350 185 34.54 222 185 353 196 34.56 219 190 384 219 34.58 240 188 384 199 34.6 253 199 365 237 34.62 246 196 380 180 34.64 237 193 416 216 34.66 292 202 388 228 34.68 313 174 433 222 34.7 331 231 380 246 34.72 335 213 420 256 34.74 303 216 416 246 34.76 331 246 420 196 34.78 310 225 404 250 34.8 365 219 428 276 34.82 310 246 471 262 34.84 357 199 428 259 34.86 331 259 458 272 34.88 346 225 506 296 34.9 313 225 441 250 34.92 259 266 480 240 34.94 243 231 480 272 34.96 234 259 506 279 34.98 240 262 484 299 35 202 216 471 269 35.02 185 266 462 282 35.04 177 231 502 266 35.06 180 231 497 246 35.08 193 243 437 289 35.1 182 234 484 306 35.12 204 246 441 286 35.14 204 250 428 346 35.16 193 299 400 376 35.18 219 292 404 372 35.2 213 282 408 392 35.22 246 320 420 420 35.24 256 310 396 475 35.26 276 365 339 493 35.28 250 361 384 471 35.3 259 384 380 529 35.32 282 400 335 511 35.34 292 408 353 576 35.36 272 428 357 562 35.38 269 454 350 660 35.4 292 467 376 666 35.42 320 462 328 734 35.44 320 416 380 745 35.46 320 416 369 784 35.48 328 412 396 853 35.5 320 408 369 824 35.52 317 424 365 847 35.54 324 502 376 900 35.56 282 576 369 949 35.58 292 586 353 1030 35.6 286 529 365 1069 35.62 262 396 376 992 35.64 266 353 357 924 35.66 279 306 404 767 35.68 250 292 416 581 35.7 225 266 388 502 35.72 213 199 412 441 35.74 256 210 324 365 35.76 250 154 380 317 35.78 282 149 388 266 35.8 282 164 346 250 35.82 256 159 339 237 35.84 286 144 335 458 35.86 292 177 357 256 35.88 303 130 342 222 35.9 286 149 342 240 35.92 262 132 324 246 35.94 234 137 339 210 35.96 225 128 328 216 35.98 190 130 342 190 36 166 112 299 164 36.02 174 130 313 146 36.04 146 106 342 166 36.06 137 110 320 137 36.08 130 85 324 142 36.1 132 94 328 151 36.12 135 110 342 112 36.14 112 114 324 130 36.16 149 144 289 125 36.18 130 102 328 112 36.2 121 108 310 125 36.22 142 110 320 128 36.24 151 117 289 139 36.26 146 88 335 128 36.28 135 121 324 142 36.3 137 104 361 137 36.32 146 253 324 125 36.34 149 146 346 125 36.36 135 119 317 142 36.38 161 128 331 146 36.4 146 149 353 151 36.42 169 144 365 159 36.44 161 132 365 169 36.46 154 159 380 159 36.48 144 161 357 182 36.5 159 146 353 188 36.52 169 182 424 177 36.54 177 177 396 164 36.56 182 177 376 188 36.58 159 196 380 193 36.6 159 199 420 303 36.62 154 219 412 199 36.64 151 202 420 216 36.66 182 193 404 216 36.68 169 193 437 210 36.7 169 210 424 207 36.72 161 185 449 213 36.74 166 213 416 243 36.76 166 177 433 219 36.78 177 185 412 225 36.8 185 190 404 219 36.82 182 154 408 202 36.84 216 132 449 207 36.86 174 164 400 213 36.88 222 144 428 190 36.9 207 130 437 161 36.92 250 164 388 177 36.94 225 137 420 149 36.96 204 149 412 199 36.98 207 139 428 180 37 225 164 408 182 37.02 228 151 416 169 37.04 231 142 404 177 37.06 219 156 388 207 37.08 219 139 433 196 37.1 234 123 412 199 37.12 207 130 353 182 37.14 234 128 388 177 37.16 216 121 396 144 37.18 216 125 400 161 37.2 193 121 416 154 37.22 207 125 404 159 37.24 234 149 392 164 37.26 225 149 376 174 37.28 222 142 424 182 37.3 216 117 384 177 37.32 234 156 369 166 37.34 228 159 365 216 37.36 237 174 372 196 37.38 243 164 350 182 37.4 276 177 392 199 37.42 262 156 369 196 37.44 279 210 420 234 37.46 266 202 384 243 37.48 225 202 357 250 37.5 243 207 361 259 37.52 222 228 361 292 37.54 202 225 392 289 37.56 177 269 408 331 37.58 207 243 346 317 37.6 169 262 376 331 37.62 177 234 357 339 37.64 137 225 372 299 37.66 139 234 357 350 37.68 161 216 408 335 37.7 142 234 365 240 37.72 146 237 372 250 37.74 156 225 384 216 37.76 146 204 357 240 37.78 190 188 412 246 37.8 159 182 396 231 37.82 202 196 408 219 37.84 193 207 412 234 37.86 172 199 392 250 37.88 172 199 408 250 37.9 177 196 384 231 37.92 193 177 392 222 37.94 169 169 380 246 37.96 177 196 400 222 37.98 185 202 408 243 38 193 180 376 207 38.02 177 174 388 199 38.04 177 172 384 210 38.06 156 161 380 177 38.08 219 161 404 159 38.1 169 159 380 172 38.12 166 169 392 166 38.14 199 177 396 199 38.16 202 154 392 185 38.18 225 172 404 169 38.2 282 196 412 182 38.22 213 169 388 196 38.24 180 169 365 185 38.26 269 174 350 196 38.28 199 199 384 174 38.3 193 182 412 185 38.32 202 185 384 199 38.34 199 185 380 202 38.36 202 156 369 219 38.38 237 151 324 174 38.4 292 166 369 169 38.42 266 199 388 196 38.44 253 199 380 182 38.46 262 166 380 196 38.48 246 182 424 188 38.5 259 199 392 180 38.52 222 202 404 213 38.54 231 182 392 219 38.56 225 188 372 185 38.58 234 210 369 199 38.6 246 219 412 196 38.62 259 193 396 199 38.64 262 207 400 228 38.66 231 231 404 250 38.68 286 210 400 259 38.7 219 199 372 222 38.72 216 193 384 225 38.74 193 142 396 219 38.76 196 196 328 207 38.78 213 166 384 188 38.8 199 164 384 202 38.82 193 159 361 196 38.84 193 139 369 190 38.86 174 132 369 177 38.88 169 132 380 174 38.9 169 156 372 188 38.92 151 130 346 149 38.94 154 144 388 190 38.96 142 139 380 210 38.98 159 159 361 188 39 159 146 365 216 39.02 159 159 357 207 39.04 182 149 320 216 39.06 164 135 346 219 39.08 146 151 320 210 39.1 142 151 339 234 39.12 169 149 331 188 39.14 156 137 331 190 39.16 174 151 353 177 39.18 144 135 335 177 39.2 161 110 335 154 39.22 174 144 303 154 39.24 149 139 335 185 39.26 154 119 317 139 39.28 164 108 328 125 39.3 146 144 299 139 39.32 177 100 339 130 39.34 169 128 342 161 39.36 182 121 320 121 39.38 188 128 299 128 39.4 199 121 317 130 39.42 172 125 296 112 39.44 174 132 331 154 39.46 204 144 313 132 39.48 188 119 380 149 39.5 182 149 365 128 39.52 169 108 350 156 39.54 182 125 369 139 39.56 207 137 365 142 39.58 174 137 369 144 39.6 185 154 342 142 39.62 199 144 388 164 39.64 204 130 384 144 39.66 207 149 372 149 39.68 219 149 428 128 39.7 188 144 396 149 39.72 182 128 384 130 39.74 196 125 408 180 39.76 174 142 396 135 39.78 180 125 388 154 39.8 164 156 433 177 39.82 182 128 384 137 39.84 161 125 369 142 39.86 174 132 416 132 39.88 151 125 388 142 39.9 146 114 408 130 39.92 142 151 408 112 39.94 164 137 400 151 39.96 182 114 416 144 39.98 199 125 388 144 40 196 125 416 130 40.02 193 135 396 135 40.04 213 135 380 144 40.06 234 151 404 144 40.08 231 159 424 142 40.1 240 149 412 137 40.12 256 144 400 151 40.14 231 130 384 156 40.16 279 146 424 142 40.18 317 139 372 161 40.2 335 156 404 135 40.22 342 164 396 149 40.24 335 172 388 149 40.26 342 159 396 169 40.28 357 180 376 164 40.3 433 149 392 159 40.32 424 156 388 156 40.34 437 177 384 151 40.36 412 149 396 159 40.38 396 172 400 156 40.4 424 164 428 144 40.42 454 151 404 128 40.44 428 149 408 144 40.46 388 154 392 161 40.48 282 185 420 262 40.5 303 139 380 151 40.52 292 154 392 149 40.54 286 180 392 174 40.56 269 149 380 156 40.58 237 161 380 185 40.6 225 174 384 164 40.62 234 154 416 177 40.64 219 164 400 185 40.66 237 199 388 164 40.68 213 193 396 159 40.7 199 196 416 190 40.72 222 219 412 169 40.74 234 196 369 177 40.76 222 207 404 182 40.78 361 228 384 169 40.8 193 240 396 188 40.82 196 213 384 180 40.84 240 231 384 199 40.86 231 243 412 207 40.88 266 237 388 213 40.9 234 292 396 222 40.92 253 259 392 231 40.94 282 289 396 225 40.96 303 292 404 250 40.98 303 296 412 250 41 317 299 400 237 41.02 286 328 449 246 41.04 262 306 404 240 41.06 289 262 408 213 41.08 328 266 396 231 41.1 339 253 384 231 41.12 310 246 408 231 41.14 286 243 400 225 41.16 292 240 392 222 41.18 250 182 400 199 41.2 246 296 416 174 41.22 228 188 400 182 41.24 210 185 388 174 41.26 207 193 400 193 41.28 193 180 416 164 41.3 193 188 380 193 41.32 169 193 404 180 41.34 174 185 428 210 41.36 180 182 433 182 41.38 199 177 458 225 41.4 177 185 454 193 41.42 174 185 467 164 41.44 185 172 441 169 41.46 193 199 471 213 41.48 199 193 445 193 41.5 213 204 467 182 41.52 207 190 484 210 41.54 196 202 462 185 41.56 202 182 488 228 41.58 216 166 475 182 41.6 193 207 449 210 41.62 190 188 467 182 41.64 172 151 454 196 41.66 225 177 454 199 41.68 213 188 467 207 41.7 204 169 420 228 41.72 202 193 475 237 41.74 225 207 428 259 41.76 216 210 416 324 41.78 204 199 437 250 41.8 210 207 420 213 41.82 228 237 392 269 41.84 228 237 376 253 41.86 243 243 380 286 41.88 237 219 357 272 41.9 234 216 372 259 41.92 225 196 392 259 41.94 231 246 353 250 41.96 250 250 353 259 41.98 272 256 346 259 42 262 231 335 286 42.02 250 276 365 282 42.04 225 259 353 272 42.06 219 276 384 313 42.08 240 228 320 262 42.1 228 259 416 246 42.12 216 216 380 243 42.14 219 207 353 256 42.16 188 188 384 231 42.18 193 174 408 213 42.2 193 180 384 202 42.22 172 166 380 193 42.24 169 144 437 172 42.26 182 154 416 180 42.28 188 156 416 199 42.3 159 132 420 172 42.32 144 159 428 139 42.34 146 135 396 166 42.36 139 112 424 139 42.38 146 117 441 154 42.4 135 137 437 139 42.42 159 144 420 182 42.44 125 128 437 159 42.46 139 130 416 164 42.48 128 130 467 154 42.5 139 154 475 154 42.52 154 135 433 166 42.54 132 146 408 151 42.56 146 159 441 144 42.58 159 142 454 193 42.6 139 149 424 177 42.62 137 166 396 146 42.64 137 174 424 182 42.66 151 174 441 177 42.68 159 169 428 188 42.7 159 185 454 219 42.72 166 177 449 207 42.74 174 164 404 207 42.76 172 185 408 207 42.78 177 185 433 262 42.8 177 196 424 266 42.82 169 199 454 276 42.84 177 262 467 259 42.86 161 234 396 299 42.88 164 210 420 272 42.9 156 222 408 272 42.92 159 234 392 331 42.94 144 246 449 299 42.96 174 231 416 342 42.98 164 250 404 306 43 182 237 404 320 43.02 196 269 433 328 43.04 159 272 372 376 43.06 180 276 437 353 43.08 174 299 396 400 43.1 193 303 388 445 43.12 185 331 380 467 43.14 177 324 502 454 43.16 199 310 388 484 43.18 188 353 396 538 43.2 210 346 392 534 43.22 182 388 365 552 43.24 222 346 339 534 43.26 207 388 331 534 43.28 216 384 376 534 43.3 207 400 380 538 43.32 222 404 353 524 43.34 216 372 342 543 43.36 216 396 335 571 43.38 234 384 372 538 43.4 190 416 320 566 43.42 216 467 350 566 43.44 219 400 310 605 43.46 225 480 342 605 43.48 240 437 339 610 43.5 240 441 335 635 43.52 243 480 320 660 43.54 250 441 310 655 43.56 250 449 317 645 43.58 262 506 331 660 43.6 259 416 324 581 43.62 253 342 303 581 43.64 219 433 346 506 43.66 216 320 320 445 43.68 204 306 328 416 43.7 240 269 286 376 43.72 185 234 331 369 43.74 202 225 335 328 43.76 193 199 320 310 43.78 154 225 313 262 43.8 159 204 320 253 43.82 193 225 286 237 43.84 180 228 282 202 43.86 156 210 313 193 43.88 185 193 346 202 43.9 202 216 299 228 43.92 185 196 313 196 43.94 159 207 299 210 43.96 188 204 353 207 43.98 196 199 324 202 44 161 199 299 202 44.02 166 190 279 193 44.04 164 182 335 185 44.06 188 180 306 174 44.08 213 177 339 169 44.1 196 159 328 151 44.12 210 154 328 177 44.14 180 169 357 154 44.16 204 159 342 146 44.18 196 161 342 169 44.2 196 154 357 169 44.22 196 146 571 174 44.24 149 128 372 164 44.26 177 169 357 159 44.28 180 137 357 174 44.3 149 159 350 188 44.32 169 177 346 149 44.34 156 185 376 151 44.36 190 166 342 174 44.38 154 185 384 174 44.4 154 188 361 169 44.42 159 199 380 240 44.44 137 202 342 185 44.46 137 213 313 199 44.48 159 199 365 222 44.5 156 237 335 213 44.52 139 231 365 243 44.54 135 225 353 216 44.56 154 253 361 282 44.58 146 262 324 246 44.6 159 234 361 266 44.62 151 246 369 292 44.64 159 286 376 299 44.66 177 253 350 310 44.68 156 276 369 296 44.7 174 259 342 303 44.72 156 272 331 303 44.74 142 272 353 289 44.76 180 240 324 328 44.78 177 266 339 286 44.8 166 272 342 286 44.82 149 262 328 282 44.84 151 237 339 286 44.86 132 246 342 292 44.88 146 276 369 303 44.9 149 228 384 299 44.92 125 262 350 310 44.94 149 234 350 279 44.96 144 266 353 303 44.98 144 193 350 262 45 156 196 317 286 45.02 146 199 350 231 45.04 156 185 331 213 45.06 159 161 306 210 45.08 149 174 299 202 45.1 151 156 310 182 45.12 144 144 296 180 45.14 161 151 317 164 45.16 169 166 320 146 45.18 166 180 289 169 45.2 177 180 286 172 45.22 169 146 328 174 45.24 185 159 269 169 45.26 188 139 306 149 45.28 169 159 310 177 45.3 190 169 320 185 45.32 190 151 292 161 45.34 188 166 289 182 45.36 182 146 286 202 45.38 193 172 306 193 45.4 196 193 289 172 45.42 182 161 276 193 45.44 172 177 317 188 45.46 169 188 272 196 45.48 185 149 262 219 45.5 156 135 296 199 45.52 159 169 279 174 45.54 169 154 317 182 45.56 177 154 272 166 45.58 164 154 289 164 45.6 174 149 276 149 45.62 161 156 289 193 45.64 172 164 266 180 45.66 188 154 266 213 45.68 151 172 299 188 45.7 149 213 276 164 45.72 207 169 299 193 45.74 237 180 279 213 45.76 199 188 296 196 45.78 196 190 272 196 45.8 185 219 282 193 45.82 204 204 296 202 45.84 172 219 279 207 45.86 185 210 272 204 45.88 216 193 276 219 45.9 196 188 286 237 45.92 196 188 276 219 45.94 225 225 292 213 45.96 240 204 286 222 45.98 174 193 296 234 46 169 199 292 213 46.02 166 166 266 216 46.04 193 164 269 243 46.06 185 331 269 240 46.08 161 146 292 219 46.1 164 159 259 190 46.12 159 154 243 231 46.14 139 135 262 216 46.16 289 128 250 161 46.18 185 128 262 164 46.2 159 135 286 185 46.22 151 137 292 161 46.24 169 130 299 156 46.26 154 114 286 139 46.28 137 117 299 125 46.3 137 117 286 137 46.32 135 137 296 125 46.34 132 144 282 130 46.36 121 182 303 137 46.38 156 125 262 142 46.4 139 139 286 154 46.42 144 119 292 130 46.44 142 154 299 137 46.46 125 137 276 156 46.48 130 149 289 161 46.5 132 154 272 161 46.52 130 159 266 154 46.54 154 154 259 156 46.56 121 166 292 142 46.58 149 142 282 135 46.6 154 154 269 142 46.62 161 159 276 159 46.64 161 146 276 161 46.66 149 142 272 166 46.68 149 169 299 164 46.7 174 154 286 154 46.72 151 172 276 146 46.74 159 139 259 135 46.76 159 144 246 169 46.78 159 146 292 159 46.8 128 149 282 180 46.82 142 159 262 154 46.84 154 142 246 156 46.86 137 161 243 174 46.88 125 139 262 142 46.9 146 159 237 164 46.92 130 142 243 156 46.94 137 144 266 125 46.96 132 159 228 164 46.98 151 149 253 156 47 117 180 269 164 47.02 123 177 259 154 47.04 146 199 250 159 47.06 128 180 234 172 47.08 125 154 228 177 47.1 144 177 250 185 47.12 130 180 243 174 47.14 121 177 269 177 47.16 144 204 228 193 47.18 137 188 266 169 47.2 130 180 240 164 47.22 154 174 240 185 47.24 144 180 259 182 47.26 169 190 253 180 47.28 164 159 262 182 47.3 193 166 216 166 47.32 166 174 259 172 47.34 182 164 222 174 47.36 161 149 231 169 47.38 164 151 243 156 47.4 174 139 234 182 47.42 182 159 256 169 47.44 182 139 225 161 47.46 188 123 259 159 47.48 193 156 262 159 47.5 164 125 240 154 47.52 188 121 262 166 47.54 185 132 237 161 47.56 193 142 219 149 47.58 177 137 250 159 47.6 177 144 237 159 47.62 156 123 228 172 47.64 164 144 237 172 47.66 159 130 259 190 47.68 161 139 246 180 47.7 161 130 237 169 47.72 151 156 225 213 47.74 154 156 262 216 47.76 130 144 237 185 47.78 130 130 234 174 47.8 123 164 246 210 47.82 156 121 210 188 47.84 137 130 253 149 47.86 146 123 250 164 47.88 137 121 243 174 47.9 164 128 231 135 47.92 151 139 246 121 47.94 144 135 228 146 47.96 149 110 259 144 47.98 142 121 272 121 48 132 119 253 132 48.02 132 121 240 149 48.04 139 110 243 144 48.06 132 96 272 137 48.08 125 135 256 135 48.1 130 121 253 144 48.12 123 112 282 128 48.14 142 100 253 123 48.16 137 123 259 146 48.18 125 125 272 123 48.2 130 119 262 128 48.22 146 100 246 149 48.24 139 132 259 121 48.26 137 110 240 137 48.28 139 114 292 130 48.3 151 137 266 128 48.32 161 149 289 130 48.34 177 130 269 154 48.36 144 114 286 149 48.38 180 121 259 128 48.4 149 146 296 159 48.42 156 144 262 154 48.44 121 151 266 159 48.46 166 139 266 135 48.48 144 193 231 169 48.5 154 154 253 164 48.52 132 154 269 166 48.54 135 151 276 159 48.56 139 161 246 161 48.58 117 164 282 166 48.6 128 159 272 180 48.62 128 182 266 169 48.64 137 142 289 174 48.66 128 169 266 172 48.68 123 161 246 188 48.7 102 137 222 180 48.72 125 142 253 164 48.74 135 159 256 159 48.76 121 130 243 135 48.78 159 110 256 151 48.8 135 137 240 151 48.82 121 119 262 149 48.84 135 130 231 142 48.86 149 121 240 130 48.88 132 121 253 132 48.9 123 114 234 128 48.92 149 114 234 130 48.94 144 135 237 108 48.96 166 102 246 117 48.98 137 128 272 102 49 137 128 225 128 49.02 130 108 237 125 49.04 146 117 225 117 49.06 149 108 213 135 49.08 142 94 246 114 49.1 144 112 256 123 49.12 137 100 219 121 49.14 151 117 237 121 49.16 146 106 190 137 49.18 156 104 213 117 49.2 130 112 216 130 49.22 128 92 234 130 49.24 135 123 240 135 49.26 121 130 207 135 49.28 132 128 216 132 49.3 117 108 207 135 49.32 135 108 225 149 49.34 128 98 216 154 49.36 137 130 204 151 49.38 125 110 240 151 49.4 110 125 243 146 49.42 121 130 234 219 49.44 121 114 219 151 49.46 119 92 213 156 49.48 137 130 202 149 49.5 144 123 240 121 49.52 102 123 216 117 49.54 117 117 225 151 49.56 114 130 228 139 49.58 108 149 222 128 49.6 112 121 207 139 49.62 110 110 210 139 49.64 123 128 210 137 49.66 100 119 222 137 49.68 92 121 213 149 49.7 135 128 237 110 49.72 121 110 193 130 49.74 119 119 207 139 49.76 128 112 207 128 49.78 108 132 225 121 49.8 104 130 222 125 49.82 106 108 199 121 49.84 119 137 222 130 49.86 100 135 207 144 49.88 112 104 222 137 49.9 114 132 225 130 49.92 102 112 210 137 49.94 92 94 204 161 49.96 121 102 202 123 49.98 98 100 196 125 50

TABLE B 2θ and d-spacing values of the significant XRPD peaks shown by arrows in FIG. 15 for smilagenin in form VI (smilagenin channel hydrate). Angle (2θ)/° d/Å Relative intensity (%) 3.463 25.49368 3.0 3.930 22.46393 7.1 6.467 13.65546 15.6 7.000 12.61750 3.6 7.851 11.25135 11.3 8.667 10.19453 3.2 10.130 8.72471 8.3 11.213 7.88477 3.5 11.844 7.46603 4.2 12.421 7.11998 8.7 13.007 6.80100 12.1 13.642 6.48582 20.4 13.959 6.33900 42.5 14.236 6.21630 29.5 14.625 6.05196 28.8 15.059 5.87850 23.5 15.566 5.68787 15.5 16.550 5.35198 24.2 16.900 5.24192 48.0 17.221 5.14492 100.0 17.818 4.97399 26.7 18.377 4.82384 34.3 19.354 4.58246 18.7 19.752 4.49103 19.8 20.312 4.36847 26.0 21.837 4.06663 16.2 23.125 3.84295 19.7 23.630 3.76205 15.8 24.904 3.57235 11.7 25.868 3.44136 17.0 26.540 3.35581 13.2 27.100 3.28765 12.4 The relative intensity of each peak as a percentage of the intensity of the strongest peak is also shown. λ is 1.5406 Å and the 2θ range is 2.4° to 27.5°. The measurements were conducted at 25° C. (room temperature).

TABLE C 2θ and d-spacing values of the significant XRPD peaks shown by arrows in FIG. 16 for smilagenin in form VII (smilagenin IPA solvate). Angle (2θ)/° d/Å Relative intensity (%) 6.459 13.67403 43.0 7.184 12.29531 18.4 10.215 8.65248 11.5 11.581 7.63461 25.4 12.639 6.99803 73.1 13.030 6.78879 100.0 13.658 6.47790 61.2 14.176 6.24260 93.2 15.150 5.84325 53.7 15.534 5.69963 82.5 16.378 5.40768 67.2 16.700 5.30424 56.8 17.276 5.12881 53.3 18.129 4.88935 51.4 18.820 4.71129 65.6 19.316 4.59146 60.0 20.334 4.36377 66.7 22.965 3.86941 44.9 23.523 3.77887 42.3 24.752 3.59400 37.5 25.448 3.49721 39.3 The relative intensity of each peak as a percentage of the intensity of the strongest peak is also shown. λ is 1.5406 Å and the 2θ range is 2.4° to 27.5°. The measurements were conducted at 25° C. (room temperature).

The foregoing broadly describes the present invention without limitation. Variations and modifications as will be readily apparent to those of ordinary skill in this art are intended to be covered by the present application and resultant patent(s). 

1-7. (canceled)
 8. Smilagenin channel hydrate.
 9. Smilagenin monohydrate.
 10. Smilagenin hydrate at a hydration stoichiometry other than 1:1. 11-46. (canceled)
 47. A material according to claim 8, substantially free of another form of smilagenin.
 48. A material according to claim 8, substantially free of other steroidal sapogenins.
 49. A material according to claim 8, substantially free of other steroidal saponins.
 50. A material according to claim 9, substantially free of another form of smilagenin.
 51. A material according to claim 9, substantially free of other steroidal sapogenins.
 52. A material according to claim 9, substantially free of other steroidal saponins.
 53. A material according to claim 10, substantially free of another form of smilagenin.
 54. A material according to claim 10, substantially free of other steroidal sapogenins.
 55. A material according to claim 10, substantially free of other steroidal saponins.
 56. A material according to claim 8 in at least about 50% by weight pure form.
 57. A material according to claim 8 in at least about 90% by weight pure form.
 58. A material according to claim 8 in at least about 95% by weight pure form.
 59. A material according to claim 8 in substantially pure isolated form prepared on a kilogram scale.
 60. A material according to claim 9 in at least about 50% by weight pure form.
 61. A material according to claim 9 in at least about 90% by weight pure form.
 62. A material according to claim 9 in at least about 95% by weight pure form.
 63. A material according to claim 9 in substantially pure isolated form prepared on a kilogram scale.
 64. A material according to claim 10 in at least about 50% by weight pure form.
 65. A material according to claim 10 in at least about 90% by weight pure form.
 66. A material according to claim 10 in at least about 95% by weight pure form.
 67. A material according to claim 10 in substantially pure isolated form prepared on a kilogram scale. 